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.io.*;
import java.util.*;
import java.text.*;
import java.lang.*;
import java.math.*;

public class Solution{
	
	public void solve () throws IOException  {
       
    	
		InputReader in = new InputReader(System.in);
		PrintWriter pw = new PrintWriter(System.out);
        int t = in.nextInt();
        
        while(t-- > 0){
        	int n = in.nextInt();
        	long k = in.nextLong();
        	long l = in.nextLong();
        	long d[] = new long [n];
        	for(int i = 0 ; i < n ; i++)
        	{
        		d[i] = l - in.nextLong();
        	}
        	long start = k;
			int parity = 1;
			boolean chk = true;
        	for(int i = 0 ; i < n ; i++) {
        		if(d[i] >= k) {
        		     start = k - 1;
        			 parity = 1;
        		}
        		else if(d[i] < 0) {
        			chk = false;
        		}
        		else {
        			if(parity == 1) {
        				if(d[i] >= start) {
        					start--;
        				}
        				else {
        					start = d[i] - 1;
        				}
        			}
        			else {
        				if(d[i] >= start) {
        					start++;
        				}
        				else {
        					chk = false;
        				}
        			}
        			if(start < 0) {
        				start = 1;
        				parity = 0;
        			}
        		}
        	}
        	if(chk){
        		pw.println("Yes");
        	}
        	else {
        		pw.println("No");
        	}
        	
        }
        pw.flush(); 
        pw.close();
    }
    public static void main(String[] args) throws Exception {
        
         
        new Thread(null,new Runnable() {
            public void run() {
                  try {
					new Solution().solve();
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
            }  
        },"1",1<<26).start();
        
        
    }
   
    static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
        }
        
        static class InputReader 
        {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) 
        {
            this.stream = stream;
        }
        public int snext() 
        {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) 
            {
                curChar = 0;
                try 
                {
                    snumChars = stream.read(buf);
                } 
                catch (IOException e) 
                {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() 
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = snext();
            }
            int res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public long nextLong()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = snext();
            }
            long res = 0;
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
            return res * sgn;
        }
 
        public int[] nextIntArray(int n) 
        {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) 
            {
                a[i] = nextInt();
            }
            return a;
        }
 
        public String readString()
        {
            int c = snext();
            while (isSpaceChar(c)) 
            {
                c = snext();
            }
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public String nextLine() 
        {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = snext();
            } while (!isEndOfLine(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) 
        {
            return c == '\n' || c == '\r' || c == -1;
        }
 
        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }
        public static long mod = 1000000007;
        public static int d;
        public static int p;
        public static int q;
        public void extended(int a,int b) {
            if(b==0) {
                d=a;
                p=1;
                q=0;
            }
            else
            {
                extended(b,a%b);
                int temp=p;
                p=q;
                q=temp-(a/b)*q;
            }
        }
       
        
        public static long binaryExponentiation(long x,long n)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
        public static long[] shuffle(long[] a,Random gen)
        {
            int n = a.length;
            for(int i=0;i<n;i++)
            {
                int ind = gen.nextInt(n-i)+i;
                long temp = a[ind];
                a[ind] = a[i];
                a[i] = temp;
            }
            return a;
        }
        
        public static void swap(int a, int b){
            int temp = a;
            a = b;
            b = temp;
        }
        
        public static HashSet<Integer> primeFactorization(int n)
        {
            HashSet<Integer> a =new HashSet<Integer>();
            for(int i=2;i*i<=n;i++)
            {
                while(n%i==0)
                {
                    a.add(i);
                    n/=i;
                }
            }
            if(n!=1)
                a.add(n);
            return a;
        }
        
        public static void sieve(boolean[] isPrime,int n)
        {
            for(int i=1;i<n;i++)
                isPrime[i] = true;
            
            isPrime[0] = false;
            isPrime[1] = false;
            
            for(int i=2;i*i<n;i++)
            {
                if(isPrime[i] == true)
                {
                    for(int j=(2*i);j<n;j+=i)
                        isPrime[j] = false;
                }
            }
        }
        
        public static long GCD(long n,long m)
        {
            if(m==0)
                return n;
            else
                return GCD(m,n%m);
        }
        public static long LCM (long a,long b) {
            return ((a*b)/(GCD(a,b)));
        }
        
        static class pair implements Comparable<pair>
        {
            Integer y ;
            Long x ;
            
            pair(long  l, int w )
            {
                this.x=l;
                this.y=w;
            }

           
            public int compareTo(pair o) {
                int result = x.compareTo(o.x);
                if(result==0)
                    result = y.compareTo(o.y);
                
                return result;
            }  
            
            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 x.hashCode()*3 +  y.hashCode();
                
            }
        }
        public static int binaryExponentiation(int x,int n)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=result * x;
                x=x*x;
                n=n/2;
            }
            return result;
        }
        
       
        
        public static int modularExponentiation(int x,int n,int M)
        {
            int result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result * x)%M;
                x=(x%M*x)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modularExponentiation(long x,long n,long M)
        {
            long result=1;
            while(n>0)
            {
                if(n % 2 ==1)
                    result=(result%M * x%M)%M;
                x=(x%M * x%M)%M;
                n=n/2;
            }
            return result;
        }
        
        public static long modInverse(int A,int M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
        public static long modInverse(long A,long M)
        {
            return modularExponentiation(A,M-2,M);
        }
        
       
        
                    
         
}
