The only difference between easy and hard versions is on constraints. In this version constraints are higher. You can make hacks only if all versions of the problem are solved.

Koa the Koala is at the beach!

The beach consists (from left to right) of a shore, n+1 meters of sea and an island at n+1 meters from the shore.

She measured the depth of the sea at 1, 2, ..., n meters from the shore and saved them in array d. d_i denotes the depth of the sea at i meters from the shore for 1 ≤ i ≤ n.

Like any beach this one has tide, the intensity of the tide is measured by parameter k and affects all depths from the beginning at time t=0 in the following way:

  * For a total of k seconds, each second, tide increases all depths by 1.

  * Then, for a total of k seconds, each second, tide decreases all depths by 1.

  * This process repeats again and again (ie. depths increase for k seconds then decrease for k seconds and so on ...).

Formally, let's define 0-indexed array p = [0, 1, 2, …, k - 2, k - 1, k, k - 1, k - 2, …, 2, 1] of length 2k. At time t (0 ≤ t) depth at i meters from the shore equals d_i + p[t mod 2k] (t mod 2k denotes the remainder of the division of t by 2k). Note that the changes occur instantaneously after each second, see the notes for better understanding. 




At time t=0 Koa is standing at the shore and wants to get to the island. Suppose that at some time t (0 ≤ t) she is at x (0 ≤ x ≤ n) meters from the shore:

  * In one second Koa can swim 1 meter further from the shore (x changes to x+1) or not swim at all (x stays the same), in both cases t changes to t+1.

  * As Koa is a bad swimmer, the depth of the sea at the point where she is can't exceed l at integer points of time (or she will drown). More formally, if Koa is at x (1 ≤ x ≤ n) meters from the shore at the moment t (for some integer t≥ 0), the depth of the sea at this point — d_x + p[t mod 2k] — can't exceed l. In other words, d_x + p[t mod 2k] ≤ l must hold always.

  * Once Koa reaches the island at n+1 meters from the shore, she stops and can rest.

Note that while Koa swims tide doesn't have effect on her (ie. she can't drown while swimming). Note that Koa can choose to stay on the shore for as long as she needs and neither the shore or the island are affected by the tide (they are solid ground and she won't drown there). 




Koa wants to know whether she can go from the shore to the island. Help her!

Input

The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows.

The first line of each test case contains three integers n, k and l (1 ≤ n ≤ 3 ⋅ 10^5; 1 ≤ k ≤ 10^9; 1 ≤ l ≤ 10^9) — the number of meters of sea Koa measured and parameters k and l.

The second line of each test case contains n integers d_1, d_2, …, d_n (0 ≤ d_i ≤ 10^9) — the depths of each meter of sea Koa measured.

It is guaranteed that the sum of n over all test cases does not exceed 3 ⋅ 10^5.

Output

For each test case:

Print Yes if Koa can get from the shore to the island, and No otherwise.

You may print each letter in any case (upper or lower).

Example

Input


7
2 1 1
1 0
5 2 3
1 2 3 2 2
4 3 4
0 2 4 3
2 3 5
3 0
7 2 3
3 0 2 1 3 0 1
7 1 4
4 4 3 0 2 4 2
5 2 3
1 2 3 2 2


Output


Yes
No
Yes
Yes
Yes
No
No

Note

In the following s denotes the shore, i denotes the island, x denotes distance from Koa to the shore, the underline denotes the position of Koa, and values in the array below denote current depths, affected by tide, at 1, 2, ..., n meters from the shore.

In test case 1 we have n = 2, k = 1, l = 1, p = [ 0, 1 ].

Koa wants to go from shore (at x = 0) to the island (at x = 3). Let's describe a possible solution:

  * Initially at t = 0 the beach looks like this: [\underline{s}, 1, 0, i]. 
  * At t = 0 if Koa would decide to swim to x = 1, beach would look like: [s, \underline{2}, 1, i] at t = 1, since 2 > 1 she would drown. So Koa waits 1 second instead and beach looks like [\underline{s}, 2, 1, i] at t = 1. 
  * At t = 1 Koa swims to x = 1, beach looks like [s, \underline{1}, 0, i] at t = 2. Koa doesn't drown because 1 ≤ 1. 
  * At t = 2 Koa swims to x = 2, beach looks like [s, 2, \underline{1}, i] at t = 3. Koa doesn't drown because 1 ≤ 1. 
  * At t = 3 Koa swims to x = 3, beach looks like [s, 1, 0, \underline{i}] at t = 4. 
  * At t = 4 Koa is at x = 3 and she made it! 



We can show that in test case 2 Koa can't get to the island.
import java.util.*;

import org.ietf.jgss.GSSManager;

import java.awt.GridBagConstraints;
import java.awt.geom.AffineTransform;
import java.io.*;
import java.lang.reflect.Member;

   public class Main {

    public static void main(String[] args) throws Exception {
    	int t=sc.nextInt();
    	while(t-->0) {
    		int n=sc.nextInt();
    		int k=sc.nextInt();
    		int l=sc.nextInt();
    		int[]a=sc.nextIntArray(n);
//    		int[] change=new int[2*k];
//    		for(int i=0;i<2*k;i++) {
//    			if(i<=k) {
//    				change[i]=i;
//    			}else {
//					change[i]=2*k-i;
//				}
//    		}
    		boolean can=true;
    		boolean[]safe=new boolean[n];
    		for(int i=0;i<n;i++) {
    			if(a[i]>l) {
    				can=false;
    			}
    			if(a[i]+k<=l) {
    				safe[i]=true;
    			}
    		}
    		int cur=0;
            int val=-1;
    		for(int i=0;i<n;i++) {
    			if(safe[i]) {
    				val=-1;
    				continue;
    			}else {
					if(val==-1) {
						val=k-(l-a[i]);
//						val=(2*k-val)%(2*k);
						
					}else {
						int val3=k-(l-a[i]);
//						val3=(2*k-val3)%(2*k);
						val=Math.max(val+1, val3);
					}
					
					int val2=(val<=k?k-val:val-k);
//					pw.println(val2+" "+val);
					if(a[i]+val2>l) {
						can=false;
					}
				}
    			
    			
    		}
    		pw.println(can?"Yes":"No");
    	}
    	
    	
    	
       pw.close();
    }
    

//    public static class SegmentTree {		// 1-based DS, OOP
//    	
//    	int N; 			//the number of elements in the array as a power of 2 (i.e. after padding)
//    	long[] array ;
//    	long[] sTree;
//    	long[] lazy;
//    	
//    	SegmentTree(long[] a)		
//    	{
//    		
//    		int nn = a.length;
//    		int NN = 1; while(NN < nn) NN <<= 1; //padding
//    		
//    		long[] in = new long[NN + 1];
//    		for(int i = 1; i <= nn; i++)
//    			in[i] = a[i-1];
//    		
//    		array = in;
//    		N = in.length - 1;
//    		sTree = new long[N<<1];		//no. of nodes = 2*N - 1, we add one to cross out index zero
//    		lazy = new long[N<<1];
//    		build(1,1,N);
//    	}
//    	SegmentTree(int[] a)		
//    	{
//    		
//    		int nn = a.length;
//    		int NN = 1; while(NN < nn) NN <<= 1; //padding
//    		
//    		long[] in = new long[NN + 1];
//    		
//    		for(int i = 1; i <= nn; i++)
//    			in[i] = a[i-1];
//    		
//    		array = in;
//    		N = in.length - 1;
//    		sTree = new long[N<<1];		//no. of nodes = 2*N - 1, we add one to cross out index zero
//    		
//    		lazy = new long[N<<1];
//    		
//    		build(1,1,N);
//    	}
//    	
//    	void build(int node, int b, int e)	// O(n)
//    	{
//    		if(b == e)		{			
//    			sTree[node] = array[b];
//    		 
//    		}
//    		else						
//    		{
//    			int mid = b + e >> 1;
//    			build(node<<1,b,mid);
//    			build(node<<1|1,mid+1,e);
//    			sTree[node] = sTree[node<<1]+sTree[node<<1|1];
//    			
//    		
//    		}
//    	}
//    	
//    	
//    	void update_point(int index, long val)			// O(log n)
//    	{
//    		index += N;				
//    		sTree[index] = val;			
//    		while(index>1)				
//    		{
//    			index >>= 1;
//    			sTree[index] = sTree[index<<1] + sTree[index<<1|1];	
//    				
//    		}
//    	}
//    	
//    	
//    	void update_range(int i, int j, long val)		// O(log n) 
//    	{
//    		update_range(1,1,N,i,j,val);
//    	}
//    	
//    	void update_range(int node, int b, int e, int i, int j, long val)
//    	{
//    		if(i > e || j < b)		
//    			return;
//    		if(b >= i && e <= j)		
//    		{
//    			sTree[node] += (e-b+1)*val;			
//    			lazy[node] += val;				
//    		}							
//    		else		
//    		{
//    			int mid = b + e >> 1;
//    			propagate(node, b, mid, e);
//    			update_range(node<<1,b,mid,i,j,val);
//    			update_range(node<<1|1,mid+1,e,i,j,val);
//    			sTree[node] = sTree[node<<1] + sTree[node<<1|1];		
//    		}
//    		
//    	}
//    	void propagate(int node, int b, int mid, int e)		
//    	{
//    		lazy[node<<1] += lazy[node];
//    		lazy[node<<1|1] += lazy[node];
//    		sTree[node<<1] += (mid-b+1)*lazy[node];		
//    		sTree[node<<1|1] += (e-mid)*lazy[node];		
//    		lazy[node] = 0;
//    	}
//    	
//    	long query(int i, int j)
//    	{
//    		return query(1,1,N,i+1,j+1);
//    	}
//    	
//    	long query(int node, int b, int e, int i, int j)	// O(log n)
//    	{
//    		if(i>e || j <b)
//    			return 0;		
//    		if(b>= i && e <= j)
//    			return sTree[node];
//    		int mid = b + e >> 1;
//    		propagate(node, b, mid, e);
//    		long q1 = query(node<<1,b,mid,i,j);
//    		long q2 = query(node<<1|1,mid+1,e,i,j);
//    		return q1 + q2;	
//    	   
//    				
//    	}
//    	
//    	
//    	
//    	
//    }
	static class Scanner {
		StringTokenizer st;
		BufferedReader br;
 
		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}
 
		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++)
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}
		public long[] nextlongArray(int n) throws IOException {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
		public Long[] nextLongArray(int n) throws IOException {
            Long[] a = new Long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
		public int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }
		public Integer[] nextIntegerArray(int n) throws IOException {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }
		public boolean ready() throws IOException {
			return br.ready();
		}
 
	}
 
	static class pair implements Comparable<pair> {
		long x;
		long y;
 
		public pair(long x, long y) {
			this.x = x;
			this.y = y;
		}
 
		public String toString() {
			return x + " " + y;
		}
		public boolean equals(Object o) {
            if (o instanceof pair) {
                pair p = (pair)o;
                return p.x == x && p.y == y;
            }
            return false;
        }
        public int hashCode() {
            return new Double(x).hashCode() * 31 + new Double(y).hashCode();
        }
        public int compareTo(pair other) {
        	if(this.x==other.x) {
        		return Long.compare(this.y, other.y);
        	}
			return Long.compare(this.x, other.x);
		}
	}
 
	static class tuble implements Comparable<tuble> {
		int x;
		int y;
		int z;
 
		public tuble(int x, int y, int z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}
 
		public String toString() {
			return x + " " + y + " " + z;
		}
 
		public int compareTo(tuble other) {
			if (this.x == other.x) {
				if(this.y==other.y) {
					return this.z - other.z;
				}
				return this.y - other.y;
			} else {
				return this.x - other.x;
			}
		}
	}
 
	public static long GCD(long a, long b) {
		if (b == 0)
			return a;
		if (a == 0)
			return b;
		return (a > b) ? GCD(a % b, b) : GCD(a, b % a);
	}
 
	public static long LCM(long a, long b) {
		return a * b / GCD(a, b);
	}
 
	static long Pow(long a, long e, long mod) // O(log e)
	{
		a %= mod;
		long res = 1l;
		while (e > 0) {
			if ((e & 1) == 1)
				res = (res * a) % mod;
			a = (a * a) % mod;
			e >>= 1l;
		}
		return res;
	}
   public static long modinverse(long a,long mod) {
	   return Pow(a, mod-2, mod);
   }
	static long nc(int n, int r) {
		if (n < r)
			return 0;
		long v = fac[n];
		v *= Pow(fac[r], mod - 2, mod);
		v %= mod;
		v *= Pow(fac[n - r], mod - 2, mod);
		v %= mod;
		return v;
	}
	static long np(int n,int r) {
		return (nc(n, r)*fac[r])%mod;
	}
	public static boolean isprime(long a) {
		if (a == 0 || a == 1) {
			return false;
		}
		if (a == 2) {
			return true;
		}
		for (int i = 2; i < Math.sqrt(a) + 1; i++) {
			if (a % i == 0) {
				return false;
			}
		}
		return true;
	}
 
	public static boolean isPal(String s) {
		boolean t = true;
		for (int i = 0; i < s.length(); i++) {
			if (s.charAt(i) != s.charAt(s.length() - 1 - i)) {
				t = false;
				break;
			}
		}
		return t;
	}
 
	public static long RandomPick(long[] a) {
		int n = a.length;
		int r = rn.nextInt(n);
		return a[r];
	}
 
	public static int RandomPick(int[] a) {
		int n = a.length;
		int r = rn.nextInt(n);
		return a[r];
	}
 static class hash {
	 int[]HashsArray;
	 boolean reverse;
	 int prelen;
	public  hash(String s, boolean r) {
		prelen = s.length();
		reverse=r;
		HashsArray = new int[prelen + 1];
		if (HashsArrayInd == 0) {
			int[] mods = { 1173017693, 1173038827, 1173069731, 1173086977, 1173089783, 1173092147, 1173107093,
					1173114391, 1173132347, 1173144367, 1173150103, 1173152611, 1173163993, 1173174127, 1173204679,
					1173237343, 1173252107, 1173253331, 1173255653, 1173260183, 1173262943, 1173265439, 1173279091,
					1173285331, 1173286771, 1173288593, 1173298123, 1173302129, 1173308827, 1173310451, 1173312383,
					1173313571, 1173324371, 1173361529, 1173385729, 1173387217, 1173387361, 1173420799, 1173421499,
					1173423077, 1173428083, 1173442159, 1173445549, 1173451681, 1173453299, 1173454729, 1173458401,
					1173459491, 1173464177, 1173468943, 1173470041, 1173477947, 1173500677, 1173507869, 1173522919,
					1173537359, 1173605003, 1173610253, 1173632671, 1173653623, 1173665447, 1173675577, 1173675787,
					1173684683, 1173691109, 1173696907, 1173705257, 1173705523, 1173725389, 1173727601, 1173741953,
					1173747577, 1173751499, 1173759449, 1173760943, 1173761429, 1173762509, 1173769939, 1173771233,
					1173778937, 1173784637, 1173793289, 1173799607, 1173802823, 1173808003, 1173810919, 1173818311,
					1173819293, 1173828167, 1173846677, 1173848941, 1173853249, 1173858341, 1173891613, 1173894053,
					1173908039, 1173909203, 1173961541, 1173968989, 1173999193};
			mod = RandomPick(mods);
			int[] primes = { 59, 61, 67, 71, 73, 79, 83, 89, 97, 101 };
			prime = RandomPick(primes);
			prepow = new int[1000010];
			prepow[0] = 1;
			for (int i = 1; i < 1000010; i++) {
				prepow[i] = (int) ((1l * prepow[i - 1] * prime) % mod);
				
			}
		}
		if (!reverse) {
 
			for (int i = 0; i < prelen; i++) {
				if (s.charAt(i) >= 'a' && s.charAt(i) <= 'z')
					HashsArray[i + 1] = (int) ((1l * HashsArray[i]
							+ ((1l * s.charAt(i) - 'a' + 1) *prepow[i]) % mod) % mod);
				else
					HashsArray[i + 1] = (int) ((1l * HashsArray[i]
							+ ((1l * s.charAt(i) - 'A' + 27) * prepow[i]) % mod) % mod);
			}
 
		} else {
			
			for (int i = 0; i < prelen; i++) {
				if (s.charAt(i) >= 'a' && s.charAt(i) <= 'z')
					HashsArray[i + 1] = (int) ((1l * HashsArray[i]
							+ ((1l * s.charAt(i) - 'a' + 1) * prepow[1000010 - 1 - i]) % mod) % mod);
				else
					HashsArray[i + 1] = (int) ((1l * HashsArray[i]
							+ ((1l * s.charAt(i) - 'A' + 27) * prepow[1000010 - 1 - i]) % mod) % mod);
			}
 
		}
 
		HashsArrayInd++;
 
	}
 
	public int PHV(int l, int r) {
		if (l > r) {
			return 0;
		}
		int val = (int) ((1l * HashsArray[r] + mod - HashsArray[l - 1]) % mod);
		if (!reverse) {
 
//			val = (int) ((1l * val *  modinverse(prepow[l-1], mod)) % mod);
			val = (int) ((1l * val * prepow[1000010 - l]) % mod);
		} else {
//			val = (int) ((1l * val * modinverse(prepow[prelen-r], mod)) % mod);
			
			val = (int) ((1l * val * prepow[r - 1]) % mod);
		}
		return val;
	}
 }
    public static void genprime(int n) {
    	 boolean prime[] = new boolean[n+1]; 
         for(int i=0;i<n;i++) 
             prime[i] = true; 
           
         for(int p = 2; p*p <=n; p++) 
         { 
             if(prime[p] == true) 
             { 
                 for(int i = p*p; i <= n; i += p) 
                     prime[i] = false; 
             } 
         } 
         for(int i = 2; i <= n; i++) 
         { 
             if(prime[i] == true) {
                primes.put(i,primes.size());
                primes2.put(primes2.size(),i);
             }
             
         }
    }
   
   
    public static long LSB(long x) {
		return x&-x;
	}
	static class fenwick {
		long[] arr;
		public fenwick(PriorityQueue<Integer> a) {
			PriorityQueue<Integer>q=new PriorityQueue<Integer>(a);
			arr=new long[a.size()+1];
			int i=1;
			while(!q.isEmpty()) {
				int z=q.poll();
				arr[i]+=z;
				if(i+LSB(i)<=a.size()) {
					arr[(int) (i+LSB(i))]+=arr[i];
				}
				i++;
			}
		}
		public fenwick(TreeSet<Integer> a) {
			arr=new long[a.size()+1];
			int i=1;
			for(int h:a) {
				arr[i]+=h;
				if(i+LSB(i)<=a.size()) {
					arr[(int) (i+LSB(i))]+=arr[i];
				}
				i++;
			}
		}
		public fenwick(Integer a) {
			arr=new long[a];
			
		}
		public fenwick(Integer[] a) {
			arr=new long[a.length+1];
			for(int i=1;i<=a.length;i++) {
				arr[i]+=a[i-1];
				if(i+LSB(i)<=a.length) {
					arr[(int) (i+LSB(i))]+=arr[i];
				}
			}
		}
		public fenwick(int[] a) {
			arr=new long[a.length+1];
			for(int i=1;i<=a.length;i++) {
				arr[i]+=a[i-1];
				if(i+LSB(i)<=a.length) {
					arr[(int) (i+LSB(i))]+=arr[i];
				}
			}
		}public fenwick(long[] a) {
			arr=new long[a.length+1];
			for(int i=1;i<=a.length;i++) {
				arr[i]+=a[i];
				if(i+LSB(i)<=a.length) {
					arr[(int) (i+LSB(i))]+=arr[i];
				}
			}
		}
		public void update(int ind,long x) {
			int i=ind;
			while(i<arr.length) {
				arr[i]+=x;
				i+=LSB(i);
			}
		}
		public long PrefixSum(int ind) {
			long sum=0;
			int i=ind;
			while(i>0) {
				sum+=arr[i];
				i=(int) (i-LSB(i));
			}
			return sum;
		}
		public long RangeQuerey(int l,int r) {
			return  this.PrefixSum(r+1)-this.PrefixSum(l);
		}
		public long maxConsecutiveValue(int k) {
			long max=Long.MIN_VALUE;
			for(int i=k-1;i<arr.length-1;i++) {
				
				max= Math.max(max,  this.RangeQuerey(i-k+1, i));
				
			}
			return max;
		}
		public long minConsecutiveValue(int k) {
			long min=Long.MAX_VALUE;
			
			for(int i=k-1;i<arr.length-1;i++) {
				
				min= Math.min(min,  this.RangeQuerey(i-k+1, i));
				
			}
			return min;
		}
		public long value(int ind) {
			return arr[ind];
		}
	}
	static void sieveLinear(int N)
	{
		ArrayList<Integer> primes = new ArrayList<Integer>();
		lp = new int[N + 1];								//lp[i] = least prime divisor of i
		for(int i = 2; i <= N; ++i)
		{
			if(lp[i] == 0)
			{
				primes.add(i);
				lp[i] = i;
			}
			int curLP = lp[i];
			for(int p: primes)//all primes smaller than or equal my lowest prime divisor
				if(p > curLP || p * 1l * i > N)
					break;
				else
					lp[p * i] = p;
		}
	}
	public static void primefactorization(int n) {
		int x=n;
	while(x>1) {
		int lowestDivisor=lp[x];
		while(x%lowestDivisor==0) {
			primefactors.add(lowestDivisor);
			x/=lowestDivisor;
		}
	}
	}
	public static class SuffixArray {

		int[] SA;
		int[] AS;
		String SS;
		public SuffixArray(String S)					//has a terminating character (e.g. '$')
		{
			SS=S;
			char[] s=new char[S.length()+1];
			for(int i=0;i<S.length();i++) {
				s[i]=S.charAt(i);
			}
			s[S.length()]='$';
			int n = s.length, RA[] = new int[n];
			SA = new int[n];
			
			for(int i = 0; i < n; ++i) { RA[i] = s[i]; SA[i] = i; }
			
			for(int k = 1; k < n; k <<= 1)
			{
				sort(SA, RA, n, k);
				sort(SA, RA, n, 0);
				int[] tmp = new int[n];

				for(int i = 1, r = 0, s1 = SA[0], s2; i < n; ++i)
				{
					s2 = SA[i];
					tmp[s2] = RA[s1] == RA[s2] && RA[s1 + k] == RA[s2 + k] ? r : ++r;
					s1 = s2;
				}
				for(int i = 0; i < n; ++i)
					RA[i] = tmp[i];
				
				if(RA[SA[n-1]] == n - 1)
					break;
			}
			AS=new int[SA.length];
			for(int i=0;i<SA.length;i++) {
				AS[SA[i]]=i;
			}
		}
		public String toString() {
			
			return Arrays.toString(SA);
		}
		public int get(int n) {
			return SA[n];
		}
		public int Substring(String s) {  // log(n)*|s|
			int low=0;
			int high=SA.length;
			int mid=(low+high)/2;
			int ind=-1;
			
			while(low<high-1) {
				
				if(SS.length()-SA[mid]<s.length()) {
				
					boolean less=false;
					for(int i=SA[mid];i<SS.length();i++) {
						if(SS.charAt(i)>s.charAt(i-SA[mid])) {
							less=true;
							break;
						}
						if(SS.charAt(i)<s.charAt(i-SA[mid])) {
							less=false;
							break;
						}
					}
					if(!less) {
						low=mid;
					}else {
						high=mid;
					}
				}else {
					boolean less=true;
					boolean equal=true;
					for(int i=SA[mid];i<SA[mid]+s.length();i++) {
						if(SS.charAt(i)<s.charAt(i-SA[mid])&&equal) {
							less=false;
							equal=false;
							break;
						}
						if(SS.charAt(i)!=s.charAt(i-SA[mid])){
							equal=false;
						}
					}
					if(equal) {
						ind=SA[mid];
					}
					if(!less) {
						low=mid;
					}else {
						high=mid;
					}
				}
				
				
				mid=(low+high)/2;
			}
			return ind;
		}
		public int LastSubstring(String s) {  // log(n)*|s|
			int low=0;
			int high=SA.length;
			int mid=(low+high)/2;
			int ind=-1;
			
			while(low<high-1) {
				
				if(SS.length()-SA[mid]<s.length()) {
				
					boolean less=true;
					for(int i=SA[mid];i<SS.length();i++) {
						if(SS.charAt(i)<s.charAt(i-SA[mid])) {
							break;
						}
						if(SS.charAt(i)>s.charAt(i-SA[mid])) {
							less=false;
							break;
						}
					}
					if(less) {
						low=mid;
					}else {
						high=mid;
					}
				}else {
					boolean less=true;
					boolean equal=true;
					for(int i=SA[mid];i<SA[mid]+s.length();i++) {
						if(SS.charAt(i)>s.charAt(i-SA[mid])&&equal) {
							less=false;
							equal=false;
							break;
						}
						if(SS.charAt(i)!=s.charAt(i-SA[mid])){
							equal=false;
						}
					}
					if(equal) {
						ind=SA[mid];
					}
					if(less) {
						low=mid;
					}else {
						high=mid;
					}
				}
				
				
				mid=(low+high)/2;
			}
			return ind;
		}
		public int CountSubstring(String s) {
			int z=LastSubstring(s);
			if(z==-1)
				return 0;
			return AS[z]-AS[Substring(s)]+1;
		}
		public void sort(int[] SA, int[] RA, int n, int k)
		{
			int maxi = Math.max(256, n), c[] = new int[maxi];  
			for(int i = 0; i < n; ++i)
				c[i + k < n ? RA[i + k] : 0]++;
			for(int i = 0, sum = 0; i < maxi; ++i)
			{
				int t = c[i];
				c[i] = sum;
				sum += t;
			}
			int[] tmp = new int[n];
			for(int i = 0; i < n; ++i)
			{
				int j = SA[i] + k;
				tmp[c[j < n ? RA[j] : 0]++] = SA[i];
			}
			
			for(int i = 0; i < n; ++i)
				SA[i] = tmp[i];
		}
	}
	  public static class UnionFind {                                              
	    	int[] p, rank, setSize;
	    	int numSets;

	    	public UnionFind(int N) 
	    	{
	    		p = new int[numSets = N];
	    		rank = new int[N];
	    		setSize = new int[N];
	    		for (int i = 0; i < N; i++) {  p[i] = i; setSize[i] = 1; }
	    	}

	    	public int findSet(int i) { return p[i] == i ? i : (p[i] = findSet(p[i])); }

	    	public boolean isSameSet(int i, int j) { return findSet(i) == findSet(j); }

	    	public void unionSet(int i, int j) 
	    	{ 
	    		if (isSameSet(i, j)) 
	    			return;
	    		numSets--; 
	    		int x = findSet(i), y = findSet(j);
	    		if(rank[x] > rank[y]) { p[y] = x; setSize[x] += setSize[y]; }
	    		else
	    		{	p[x] = y; setSize[y] += setSize[x];
	    			if(rank[x] == rank[y]) rank[y]++; 
	    		} 
	    	}

	    	public int numDisjointSets() { return numSets; }

	    	public int sizeOfSet(int i) { return setSize[findSet(i)]; }
	    }
	static LinkedList<Integer>primefactors=new LinkedList<>();
	static TreeMap<Integer,Integer>primes=new TreeMap<Integer, Integer>();
	static TreeMap<Integer,Integer>primes2=new TreeMap<Integer, Integer>();
	static int[]lp;
    
	
	static int HashsArrayInd = 0;
	static int[] prepow;
	static int prime = 61;
	static long fac[];
	static int mod = 1000000007;
	static Random rn = new Random();
	static Scanner sc = new Scanner(System.in);
	static PrintWriter pw = new PrintWriter(System.out);
}