Jon Snow is on the lookout for some orbs required to defeat the white walkers. There are k different types of orbs and he needs at least one of each. One orb spawns daily at the base of a Weirwood tree north of the wall. The probability of this orb being of any kind is equal. As the north of wall is full of dangers, he wants to know the minimum number of days he should wait before sending a ranger to collect the orbs such that the probability of him getting at least one of each kind of orb is at least <image>, where ε < 10 - 7.

To better prepare himself, he wants to know the answer for q different values of pi. Since he is busy designing the battle strategy with Sam, he asks you for your help.

Input

First line consists of two space separated integers k, q (1 ≤ k, q ≤ 1000) — number of different kinds of orbs and number of queries respectively.

Each of the next q lines contain a single integer pi (1 ≤ pi ≤ 1000) — i-th query.

Output

Output q lines. On i-th of them output single integer — answer for i-th query.

Examples

Input

1 1
1


Output

1


Input

2 2
1
2


Output

2
2
import java.io.BufferedWriter;
	import java.io.IOException;
	import java.io.OutputStreamWriter;
	import java.io.ObjectInputStream.GetField;
	import java.math.BigInteger;
	import java.util.ArrayList;
	import java.util.Arrays;
	import java.util.Collections;
	import java.util.HashMap;
	import java.util.HashSet;
	import java.util.InputMismatchException;
	import java.util.LinkedList;
	import java.util.List;
	import java.util.Map;
	import java.util.PriorityQueue;
	import java.util.Queue;
	import java.util.Stack;
	import java.util.TreeMap;
	import java.util.TreeSet;
	public class Q2 {
		
		static long MOD = 1000000007;
		static boolean b1,b[],bc[];
		static boolean boo[][][];
		static int ans1 = -1,ans2 = -1, root;
		static ArrayList<Integer>[] amp,amp1;
		static int sum[],dist[],cnt[];
		static long ans = 0;
		static long p = 0;
		//static ArrayList<Pair3>[][][] pmp;
		static FasterScanner sc = new FasterScanner();
		static Queue<Integer> q = new LinkedList<>();
		static int arr[],start[],end[],color[],parent[];
		static PriorityQueue<Integer> pq;
		//static ArrayList<Integer> parent = new ArrayList<>();
		static LinkedList<Integer> fa;
		static BufferedWriter log;
		static TreeMap<Integer,Integer> tm = new TreeMap<>();
		static HashSet<Pair> hs;
		static Stack<Integer> stack = new Stack<>();
		static Pair prr[];
		static long parent1[],parent2[],size[][],size1[],size2[],value[];
		public static void main(String[] args) throws Exception {
	    	soln();
	    }
		static int MAX = 10000001;
		public static void soln() throws IOException {
			log = new BufferedWriter(new OutputStreamWriter(System.out));
			int k = sc.nextInt(), q = sc.nextInt();
			double dp[][] = new double[10000][k+1];
			dp[0][0] = 1;
			double d = k;
			for(int i = 1;i<10000;i++){
				for(int j = 1;j<=k;j++){
					dp[i][j] += (dp[i-1][j-1]*(k-(j-1))/d+dp[i-1][j]*(j/d));
				}
			}
			int ans[] = new int[q];
			Pair p[] = new Pair[q];
			for(int i = 0; i< q;i++){
				p[i] = new Pair(sc.nextInt(),i);
			}
			Arrays.sort(p);
			int j = 0;
			double x = p[j].u/2000.0;
			for(int i = 1;i<10000;i++){
				while(j<q && dp[i][k]>x){
					ans[p[j].v] = i;
					j++;
					if(j>=q)break;
					x = p[j].u/2000.0;
				}
			}
			for(int i:ans) log.write(i+"\n");
			log.close();
		}
		public static void buildGraph(int n){
			for(int i =0;i<n;i++){
				int x = sc.nextInt(), y = sc.nextInt();
				amp[--x].add(--y);
				amp[y].add(x);
			}
		}
		public static void dfs2(int x){
			b[x] = true;
			for(int e:amp[x]){
				if(!b[e]){
					cnt[e] = cnt[x];
					if(hs.contains(new Pair(e+1,x+1))){
						cnt[e]++;
					}
					if(hs.contains(new Pair(x+1,e+1))){
						cnt[e]--;
					}
					dfs2(e);
				}
			}
		}
		public static void dfs(int x){
			b[x] = true;
			for(int e:amp[x]){
				if(!b[e]){
					parent[e] = x;
					dfs(e);
				}
			}
		}
		static boolean check(long arr1[] , long arr2[] , int key ,int x){
			for(int i =0 ; i< key && i<arr1.length ;i++){
				long sum = 0;
				if((key-(i+1))<=arr2.length){
					if((key-(i+1))!=0)
					sum += (arr1[i]+arr2[key-(i+1)-1]);
					else sum = arr1[i];
					if(sum<=x) return true;
				}
			}
			if(key>0 && key<=arr2.length && arr2[key-1]<=x) return true;
			return false;
		}
		public static int binarySearch(long arr[],long key){
			int low = 0, high = arr.length-1;
			while(low<high){
				int mid = (high+low+1)/2;
				if(arr[mid] >= key) low = mid;
				else high = mid-1;
			}
			if(arr[low]<key)
			return low+1;
			else return 0;
		}
		public static void bfs(int x,int arr[]){
		b = new boolean[arr.length];
		b[x] = true;
		q = new LinkedList<>();
		q.add(x);
		while(!q.isEmpty()){
			int y = q.poll();
			for(int i = 0;i<amp[y].size();i++) {
				if(!b[amp[y].get(i)]){
					q.add(amp[y].get(i));
					b[amp[y].get(i)] = true;
					arr[amp[y].get(i)] = (arr[y]+1);
				}
			}
		}
		}
		
		static long get(long x){
			if((x%10)<5) return x-(x%10);
			else return x+(10-x%10);
		}
		
		static long func(long n, long d, long t){
			return (t*(2*(n-1)+(t-1)*(d)))/2;
		}
		static class Pair implements Comparable<Pair> {
			int u;
			int v;
			public Pair(int u, int v) {
				this.u = u;
				this.v = v;
			}
			
			public int hashCode() {
				int hu = (int) (u ^ (u >>> 32));
				int hv = (int) (v ^ (v >>> 32));
				return 31*hu + hv;
			}
	 
			public boolean equals(Object o) {
				Pair other = (Pair) o;
				return (u == other.u && v == other.v);
			}
	 
			public int compareTo(Pair other) {
				return Integer.compare(u, other.u) != 0 ? (Integer.compare(u, other.u)) : (Integer.compare(v, other.v));
			}
			
			public String toString() {
				return "[u=" + u + ", v=" + v + "]";
			}
		}
		
		
		
		public static long getParent(long x, long parent[]){
			while(parent[(int) x]!=x){
				parent[(int) x] = parent[(int) parent[(int) x]];
				x = parent[(int) x];
			}
			return x;
		}
		static long min(long a, long b, long c){
			if(a<b && a<c) return a;
			if(b<c) return b;
			return c;
		}
		/*
		static void dfs3D(int x,int y,int z){
			ans++;
			boo[x][y][z] = true;
			for(Pair3 e:pmp[x][y][z]){
				if(!boo[e.x][e.y][e.z]){
					dfs3D(e.x,e.y,e.z);
				}
			}
		}
		static class Pair3{
			int x, y ,z;
			Pair3(int x, int y, int z){
				this.x = x;
				this.y = y;
				this.z = z;
			}
		}*/
		static int sum(int n){
			String str = Integer.toString(n);
			int cnt = 0;
			for(int i = 0; i< str.length();i++){
				cnt+=(str.charAt(i)-'0');
			}
			return cnt;
		}
		 static void KMPSearch(String pat, String txt)
		    {
		        int M = pat.length();
		        int N = txt.length();
		 
		        // create lps[] that will hold the longest
		        // prefix suffix values for pattern
		        int lps[] = new int[M];
		        int j = 0;  // index for pat[]
		 
		        // Preprocess the pattern (calculate lps[]
		        // array)
		        computeLPSArray(pat,M,lps);
		 
		        int i = 0;  // index for txt[]
		        while (i < N)
		        {
		            if (pat.charAt(j) == txt.charAt(i))
		            {
		                j++;
		                i++;
		            }
		            if (j == M)
		            {
		               // parent.add((i-j));
		                j = lps[j-1];
		            }
		 
		            // mismatch after j matches
		            else if (i < N && pat.charAt(j) != txt.charAt(i))
		            {
		                // Do not match lps[0..lps[j-1]] characters,
		                // they will match anyway
		                if (j != 0)
		                    j = lps[j-1];
		                else
		                    i = i+1;
		            }
		        }
		    }
		 static void computeLPSArray(String pat, int M, int lps[])
		    {
		        // length of the previous longest prefix suffix
		        int len = 0;
		        int i = 1;
		        lps[0] = 0;  // lps[0] is always 0
		 
		        // the loop calculates lps[i] for i = 1 to M-1
		        while (i < M)
		        {
		            if (pat.charAt(i) == pat.charAt(len))
		            {
		                len++;
		                lps[i] = len;
		                i++;
		            }
		            else  // (pat[i] != pat[len])
		            {
		                // This is tricky. Consider the example.
		                // AAACAAAA and i = 7. The idea is similar 
		                // to search step.
		                if (len != 0)
		                {
		                    len = lps[len-1];
		 
		                    // Also, note that we do not increment
		                    // i here
		                }
		                else  // if (len == 0)
		                {
		                    lps[i] = len;
		                    i++;
		                }
		            }
		        }
		    }
		private static void permutation(String prefix, String str) {
		    int n = str.length();
		    if (n == 0); //hs.add(prefix);
		    else {
		        for (int i = 0; i < n; i++)
		            permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n));
		    }
		}
		public static char give(char c1,char c2){
			if(c1!='a' && c2!='a') return 'a';
			if(c1!='b' && c2!='b') return 'b';
			return 'c';
		}
		static class Graph{
			int vertex;
			long weight;
		}
		public static void buildTree(int n){
			int arr[] = sc.nextIntArray(n);
			for(int i = 0;i<n;i++){
				int x = arr[i]-1;
				amp[i+1].add(x);
				amp[x].add(i+1);
			}
		}
		
		
		static class SegmentTree{
			int pre[], suf[], max[], val[];
			SegmentTree( int n){
				int size = 4*n;
				pre = new int[size];
				suf = new int[size];
				max = new int[size];
				val = new int[size];
				build(0,n-1,1);
			}
			void build(int ss, int se, int si){
				if(ss==se){
					pre[si] = 1;
					suf[si] = 1;
					max[si] = 1;
					val[si] = arr[ss];
				}
				else{
				int mid = (ss+se)>>2;
				si*=2;
				build(ss,mid,si);build(mid+1,se,si+1);
				}
			}
			
			/*int[] get(int qs, int qe, int ss, int se, int si){
				if(qe < ss || se < qs)
	        		return new int[2];
				if(qs<=ss && qe>=se){
					return new int[]{max[si],val[si]};
				}
				int mid = (ss+se)/2;
				si*=2;
				if(qe<=mid) return get(qs,qe,ss,mid,si);
				else if(qs>mid) return get(qs,qe,mid+1,se,si+1);
				long a1[] = build(ss,mid,si*2), a2[] = build(mid+1,se,si*2+1);
				long ans[] = new long[4];
				if(arr[mid] == arr[mid+1]){
				    long temp = a1[2]+a2[0];
				    if(temp>=a2[1] && temp>=a1[1]){
				        ans[1] = temp;
				        ans[3] = arr[mid];
				    }
				    else if(a2[1]>=a1[1]){
				        ans[1] = a2[1];
				        ans[3] = a2[3];
				    }
				    else{
				        ans[1] = a1[1];
				        ans[3] = a1[3];
				    } 
				    if(a1[1]==(mid-ss+1)) ans[0] = ans[1];
				    else ans[0] = a1[0];
				    if(a2[2]==(se-mid)) ans[2] = ans[1];
					else ans[2] = a2[2];
				}
				else{
					if(a2[1]>=a1[1]){
				        ans[1] = a2[1];
				        ans[3] = a2[3];
				    }
				    else{
				        ans[1] = a1[1];
				        ans[3] = a1[3];
				    } 
					ans[0] = a1[0];
					ans[2] = a2[2];
				}
	            return ans;
			}
			void print(){
				for(int i = 0;i<st.length;i++){
					System.out.println(st[i][0]+" "+st[i][1]+" "+st[i][2]+" "+st[i][3]);
				}
				System.out.println();
			}*/
		}
		static int convert(int x){
			int cnt = 0;
			String str = Integer.toBinaryString(x);
			//System.out.println(str);
			for(int i = 0;i<str.length();i++){
				if(str.charAt(i)=='1'){
					cnt++;
				}
			}
			int ans = (int) Math.pow(3, 6-cnt);
			return ans;
		}
		static class Node2{
			Node2 left = null;
			Node2 right = null;
			Node2 parent = null;
			int data;
		}
		static class BinarySearchTree{
			Node2 root = null;
			int height = 0;
			int max = 0;
			int cnt = 1;
			ArrayList<Integer> parent = new ArrayList<>();
			HashMap<Integer, Integer> hm = new HashMap<>();
			public void insert(int x){
				Node2 n = new Node2();
				n.data = x;
				if(root==null){
					root = n;
				}
				else{
					Node2 temp = root,temp2 = null;
					while(temp!=null){
						temp2 = temp;
						if(x>temp.data) temp = temp.right;
						else temp = temp.left;
					}
					if(x>temp2.data) temp2.right = n;
					else temp2.left = n;
					n.parent = temp2;
					parent.add(temp2.data);
				}
			}
			public Node2 getSomething(int x, int y, Node2 n){
				if(n.data==x || n.data==y) return n;
				else if(n.data>x && n.data<y) return n;
				else if(n.data<x && n.data<y) return getSomething(x,y,n.right);
				else return getSomething(x,y,n.left);
			}
			public Node2 search(int x,Node2 n){
				if(x==n.data){
					max = Math.max(max, n.data);
					return n;
				}
				if(x>n.data){
					max = Math.max(max, n.data);
					return search(x,n.right);
				}
				else{
					max = Math.max(max, n.data);
					return search(x,n.left);
				}
			}
			public int getHeight(Node2 n){
				if(n==null) return 0;
				height = 1+ Math.max(getHeight(n.left), getHeight(n.right));
				return height;
			}
		}
		static long findDiff(long[] arr, long[] brr, int m){
			int i = 0, j = 0;
			long fa = 1000000000000L;
			while(i<m && j<m){
				long x = arr[i]-brr[j];
				if(x>=0){
					if(x<fa) fa = x;
					j++;
				}
				else{
					if((-x)<fa) fa = -x;
					i++;
				}
			}
			return fa;
		}
		public static long max(long x, long y, long z){
			if(x>=y && x>=z) return x;
			if(y>=x && y>=z) return y;
			return z;
		}
		
		public static void seive(long n){
			b = new boolean[(int) (n+1)];
			Arrays.fill(b, true);
			for(int i = 2;i*i<=n;i++){
				if(b[i]){
					for(int p = 2*i;p<=n;p+=i){
						b[p] = false;
					}
				}
			}
		}
		static long modInverse(long a, long mOD2){
		            return  power(a, mOD2-2, mOD2);
		}
		static long power(long x, long y, long m)
		{
		    if (y == 0)
		        return 1;
		    long p = power(x, y/2, m) % m;
		    p = (p * p) % m;
		 
		    return (y%2 == 0)? p : (x * p) % m;
		}
		static long power2(long x,BigInteger y,long m){
			long ans = 1;
			BigInteger two = new BigInteger("2");
			while(y.compareTo(BigInteger.ZERO)>0){
				if(y.getLowestSetBit()==y.bitCount()){
					x = (x*x)%MOD;
					y = y.divide(two);
				}
				else{
					ans = (ans*x)%MOD;
					y = y.subtract(BigInteger.ONE);
				}
			}
			return ans;
		}
		static BigInteger power2(BigInteger x, BigInteger y, BigInteger m){
			BigInteger ans = new BigInteger("1");
			BigInteger one  = new BigInteger("1");
			BigInteger two  = new BigInteger("2");
			BigInteger zero  = new BigInteger("0");
			while(y.compareTo(zero)>0){
				//System.out.println(y);
				if(y.mod(two).equals(one)){
					ans = ans.multiply(x).mod(m);
					y = y.subtract(one);
				}
				else{
					x = x.multiply(x).mod(m);
					y = y.divide(two);
				}
			}
			return ans;
		}
		static BigInteger power(BigInteger x, BigInteger y, BigInteger m)
		{
		    if (y.equals(0))
		        return (new BigInteger("1"));
		    BigInteger p = power(x, y.divide(new BigInteger("2")), m).mod(m);
		    p = (p.multiply(p)).mod(m);
		 
		    return (y.mod(new BigInteger("2")).equals(0))? p : (p.multiply(x)).mod(m);
		}
		static long d,x,y;
		public static void extendedEuclidian(long a, long b){
			if(b == 0) {
		        d = a;
		        x = 1;
		        y = 0;
		    }
		    else {
		        extendedEuclidian(b, a%b);
		        int temp = (int) x;
		        x = y;
		        y = temp - (a/b)*y;
		    }
		}
		
		public static long gcd(long n, long m){
			if(m!=0) return gcd(m,n%m);
			else return n;
		}
		
		
		public static class FasterScanner {
			private byte[] buf = new byte[1024];
			private int curChar;
			private int numChars;
	 
			public int read() {
				if (numChars == -1)
					throw new InputMismatchException();
				if (curChar >= numChars) {
					curChar = 0;
					try {
						numChars = System.in.read(buf);
					} catch (IOException e) {
						throw new InputMismatchException();
					}
					if (numChars <= 0)
						return -1;
				}
				return buf[curChar++];
			}
	 
			public String nextLine() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = read();
				} while (!isEndOfLine(c));
				return res.toString();
			}
	 
			public String nextString() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = read();
				} while (!isSpaceChar(c));
				return res.toString();
			}
	 
			public long nextLong() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				int sgn = 1;
				if (c == '-') {
					sgn = -1;
					c = read();
				}
				long res = 0;
				do {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = read();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
	 
			public int nextInt() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				int sgn = 1;
				if (c == '-') {
					sgn = -1;
					c = read();
				}
				int res = 0;
				do {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = read();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
		        
		    public int[] nextIntArray(int n) {
		        return nextIntArray(n, 0);
		    }
		    
		    public int[] nextIntArray(int n, int off) {
		    	int[] arr = new int[n + off];
		    	for (int i = 0; i < n; i++) {
		    		arr[i + off] = nextInt();
		    	}
		    	return arr;
		    }
		    
		    public long[] nextLongArray(int n) {
		    	return nextLongArray(n, 0);
		    }
	        
			public long[] nextLongArray(int n, int off) {
			    long[] arr = new long[n + off];
			    for (int i = 0; i < n; i++) {
			        arr[i + off] = nextLong();
			    }
			    return arr;
			}
	 
		    private boolean isSpaceChar(int c) {
				return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			}
	 
			private boolean isEndOfLine(int c) {
				return c == '\n' || c == '\r' || c == -1;
			}
		}
	} 