Problem: A positive integer x is called a power of two if it can be represented as x = 2^y, where y is a non-negative integer. So, the powers of two are 1, 2, 4, 8, 16, ....

You are given two positive integers n and k. Your task is to represent n as the sum of exactly k powers of two.

Input

The only line of the input contains two integers n and k (1 ≤ n ≤ 10^9, 1 ≤ k ≤ 2 ⋅ 10^5).

Output

If it is impossible to represent n as the sum of k powers of two, print NO.

Otherwise, print YES, and then print k positive integers b_1, b_2, ..., b_k such that each of b_i is a power of two, and ∑ _{i = 1}^{k} b_i = n. If there are multiple answers, you may print any of them.

Examples

Input


9 4


Output


YES
1 2 2 4 


Input


8 1


Output


YES
8 


Input


5 1


Output


NO


Input


3 7


Output


NO

Solution (in JAVA):

Solution:

/*
 * @author romit17
 */

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class C1095 {
    
    int[] ans;
    void solve() throws IOException {
        PrintWriter out = new PrintWriter(System.out);
        StringBuilder sb = new StringBuilder("");
        int n = ni(), k = ni();
        ans = new int[35];
        if(k < Integer.bitCount(n) || k>n)
        {
            System.out.println("NO"); return;
        }
        System.out.println("YES");
        for(int i=31;i>=0;i--)
        {
            if((1<<i & n) != 0)
            {
                ans[i]++;k--;
            }
        }
        
        o:while(k!=0)
        {
            for(int i=31;i>=1;i--)
            {
                if(ans[i] == 0) continue;
                if(k<= ans[i])
                {
                    ans[i] -= k;
                    ans[i-1] += 2*k;
                    k = 0; 
                    break o;
                }
                k -= ans[i];
                ans[i-1] += 2*ans[i];
                ans[i] = 0;
            }System.out.println("u");
        }
        
        for(int i=0; i<32;i++)
        {
            int val = 1<<i;
            for(int j=0;j<ans[i];j++)
                sb.append(val+" ");
        }
        System.out.println(sb);
    }
    
    
    public static void main(String[] args) throws IOException {
        new C1095().solve();
    }    
    
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;    
    InputStream is = System.in;

    private int readByte() {
        if (lenbuf == -1) {
            throw new InputMismatchException();
        }
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) {
                return -1;
            }
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }
    
    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b));
        return b;
    }
    
    private double nd() {
        return Double.parseDouble(ns());
    }
    
    private char nc() {
        return (char) skip();
    }
    
    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) {
            map[i] = ns(m);
        }
        return map;
    }
    
    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = ni();
        }
        return a;
    }
    
    private int[] na1(int n) {
        int[] a = new int[n + 1];
        for (int i = 1; i < n + 1; i++) {
            a[i] = ni();
        }
        return a;
    }
    
    private long[] nb(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = nl();
        }
        return a;
    }
    
    private long[] nb1(int n) {
        long[] a = new long[n + 1];
        for (int i = 1; i < n + 1; i++) {
            a[i] = nl();
        }
        return a;
    }
    
    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
}