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

/**
 * @author hemenghai
 * @date 2019-01-22
 */
public class Main {

    private static int cur, pos, sum, len;
    private static int max, min, ans, res;
    private static int ai, bi, ci, di;
    private static int[] aix, bix;
    private static long al, bl, cl, dl;
    private static long[] alx, blx;
    private static double ad, bd, cd, dd;
    private static double[] adx, bdx;
    private static boolean ab, bb, cb, db;
    private static boolean[] abx, bbx;
    private static boolean[][] abxx, bbxx;
    private static char ac, bc, cc, dc;
    private static char[] acx, bcx;
    private static String as, bs, cs, ds;
    private static InputReader in = new InputReader(System.in);
    private static PrintWriter out = new PrintWriter(System.out);

    public static void main(String[] args) {
        int n = in.nextInt();
        int k = in.nextInt();
        aix = new int[32];

        for (int i = 0; i < 32; i++) {
            aix[i] = (n >> i) & 1;
            cur += aix[i];
        }

        if(k < cur || k > n){
            out.println("NO");
        } else {
            out.println("YES");
            for (int i = 31; i >= 1 && cur < k; i--) {
                ai = Math.min(k - cur, aix[i]);
                aix[i] -= ai;
                aix[i - 1] += ai * 2;
                cur += ai;
            }
            for (int i = 0; i < 31; i++) {
                ai = 1 << i;
                for (int j = 0; j < aix[i]; j++) {
                    out.printf("%d ", ai);
                }
            }
            out.println();
        }
        out.close();
    }

    private static class InputReader {

        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public String next() {
            return readString();
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E') {
                    return res * Math.pow(10, nextInt());
                }
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E') {
                        return res * Math.pow(10, nextInt());
                    }
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        private int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }
    }
}