Jamie is preparing a Codeforces round. He has got an idea for a problem, but does not know how to solve it. Help him write a solution to the following problem:

Find k integers such that the sum of two to the power of each number equals to the number n and the largest integer in the answer is as small as possible. As there may be multiple answers, you are asked to output the lexicographically largest one. 

To be more clear, consider all integer sequence with length k (a1, a2, ..., ak) with <image>. Give a value <image> to each sequence. Among all sequence(s) that have the minimum y value, output the one that is the lexicographically largest.

For definitions of powers and lexicographical order see notes.

Input

The first line consists of two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 105) — the required sum and the length of the sequence.

Output

Output "No" (without quotes) in a single line if there does not exist such sequence. Otherwise, output "Yes" (without quotes) in the first line, and k numbers separated by space in the second line — the required sequence.

It is guaranteed that the integers in the answer sequence fit the range [ - 1018, 1018].

Examples

Input

23 5


Output

Yes
3 3 2 1 0 


Input

13 2


Output

No


Input

1 2


Output

Yes
-1 -1 

Note

Sample 1:

23 + 23 + 22 + 21 + 20 = 8 + 8 + 4 + 2 + 1 = 23

Answers like (3, 3, 2, 0, 1) or (0, 1, 2, 3, 3) are not lexicographically largest.

Answers like (4, 1, 1, 1, 0) do not have the minimum y value.

Sample 2:

It can be shown there does not exist a sequence with length 2.

Sample 3:

<image>

Powers of 2:

If x > 0, then 2x = 2·2·2·...·2 (x times).

If x = 0, then 2x = 1.

If x < 0, then <image>.

Lexicographical order:

Given two different sequences of the same length, (a1, a2, ... , ak) and (b1, b2, ... , bk), the first one is smaller than the second one for the lexicographical order, if and only if ai < bi, for the first i where ai and bi differ.
import java.util.*;
import java.io.*;
import java.math.*;

public class b {


    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
     Random rand = new Random();
     //for (int ci = 0; ci < 1000; ci++) {
        long n = in.nextLong();
        long[] counts = new long[128];
        long k = in.nextLong();
        int kk = (int) k;
        for (int i = 0; i < 64; i++) {
            long bit = 1L << i;
            if ((bit & n) != 0) {
                counts[i + 64] = 1;
                k--;
            }
        }
        
        if (k < 0) {
            out.println("No");
            out.close();
            return;
        }
        //print(counts);
        for (int i = 127; i >= 1; i--) {
            long have = counts[i];
            if (have == 0) continue;
            long need = have;
            if (k >= need) {
                k -= need;
                counts[i] = 0;
                counts[i - 1] += have + need;
            } else {
                break;
            }
        }
        //print(counts);
        
        long small = -1;
        for (int i = 0; i < 128; i++) {
            if (counts[i] > 0) {
                small = i;
                break;
            }
        }
        if (k > 0)
            counts[(int) small]--;
        small -= 64;
        long[] ans = new long[kk];
        Arrays.fill(ans, 1000);
        int idx = 0;
        for (int i = 127; i >= 0; i--) {
            for (int j = 0; j < counts[i]; j++) {
                ans[idx++] = i - 64;
            }
        }
        for (int i = idx; i < kk - 1; i++) {
            small--;
            ans[i] = small;
        }
        if (idx < kk) {
            ans[kk - 1] = small;
            if (k == 0)
                System.out.println(1/0);
            if (ans[kk - 2] != ans[kk - 1])
                System.out.println(1/0);
        }
        for (long a : ans)
            if (a == 1000)
                System.out.println(1/0);
        for (int i = 1; i < kk; i++)
            if (ans[i] > ans[i - 1])
                System.out.println(1/0);
        
        out.println("Yes");
        for (int i = 0; i < kk; i++) {
            if (i > 0)
                out.print(" ");
            out.print(ans[i]);
        }
        out.println();
    //}
        
        out.close();
    }

static void print(long[] arr) {
    for (int i = 0; i < 128; i++) {
        if (arr[i] != 0)
            System.out.printf("%d: %d\n", i - 64, arr[i]);
    }
    System.out.println("------");
}
    static Random rand = new Random();
    static void sort(int[] a) {
        lsbRadixSort(a, true);
    }
    static void sort(long[] a) {
        int n = a.length;
        for (int i = a.length - 1; i > 0; i--) {
            int j = rand.nextInt(i + 1);
            long tmp = a[i];
            a[i] = a[j];
            a[j] = tmp;
        }
        Arrays.sort(a);
    }
    static void sort(double[] a) {
        int n = a.length;
        for (int i = a.length - 1; i > 0; i--) {
            int j = rand.nextInt(i + 1);
            double tmp = a[i];
            a[i] = a[j];
            a[j] = tmp;
        }
        Arrays.sort(a);
    }
    static void lsbRadixSort(int[] a, boolean signed) {
        int s = 0, n = a.length;
        int[] p = new int[257], b = new int[n];
        int sb = 1 << 31;
        if(signed) for(int i=0;i<n;i++)  a[i] ^= sb;
        while (s < 32) {
            Arrays.fill(p, 0);
            for (int i = 0; i < n; i++)
                p[((a[i] >>> s) & 255)+1]++;
            for(int i=2;i<256;i++)
                p[i] += p[i-1];
            for (int i = 0; i < n; i++)
                b[p[(a[i] >>> s) & 255]++] = a[i];
            int[] tmp = b;  b = a;  a = tmp;
            s += 8;
        }
        if(signed) for(int i=0;i<n;i++)  a[i] ^= sb;
    }
    static long gcd(long a, long b) { return b == 0 ? a : gcd(b, a % b); }
    static long lcm(long a, long b) { return a / gcd(a, b) * b; }
    static long[] eEuclid(long a, long b) {
        if (b == 0) return new long[] { a, 1, 0 };
        long[] ans = eEuclid(b, a % b);
        long temp = ans[1] - ans[2] * (a / b);
        ans[1] = ans[2];  ans[2] = temp;
        return ans;
    }
    static long modInverse(long a, long m) {
        return ((eEuclid(a, m)[1] % m) + m) % m;
    }
    static class IntList {
        static int[] EMPTY = {};
        int[] a = EMPTY;
        int n = 0;
        void add(int v) {
            if (n >= a.length)
                a = Arrays.copyOf(a, (n << 2) + 8);
            a[n++] = v;
        }
        int get(int idx) {
            return a[idx];
        }
        int size() {
            return n;
        }
    }
    static class DisjointSet {
        int[] s;
	
        public DisjointSet(int n) {
            Arrays.fill(s = new int[n], -1);
        }	
        public int find(int i) {
            return s[i] < 0 ? i : (s[i] = find(s[i]));
        }	
        public boolean union(int a, int b) {
            if ((a = find(a)) == (b = find(b))) return false;
            if(s[a] == s[b]) s[a]--;
            if(s[a] <= s[b]) s[b] = a; else s[a] = b;
            return true;
        }
    }
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        public FastScanner(InputStream i) {
            br = new BufferedReader(new InputStreamReader(i));
            st = new StringTokenizer("");
        }
        public String next() throws IOException {
            if(st.hasMoreTokens())
                return st.nextToken();
            else
                st = new StringTokenizer(br.readLine());
            return next();
        }
        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }
        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
        public int[] nextOffsetIntArray(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++)
                arr[i] = nextInt() - 1;
            return arr;
        }
        public int[] nextIntArray(int n) throws IOException {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++)
                arr[i] = nextInt();
            return arr;
        }
        public int[][] nextIntArray(int n, int m) throws IOException {
            int[][] arr = new int[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    arr[i][j] = nextInt();
            return arr;
        }
        public long[] nextLongArray(int n) throws IOException {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++)
                arr[i] = nextLong();
            return arr;
        }
        public long[][] nextLongArray(int n, int m) throws IOException {
            long[][] arr = new long[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    arr[i][j] = nextLong();
            return arr;
        }
        public double[] nextDoubleArray(int n) throws IOException {
            double[] arr = new double[n];
            for (int i = 0; i < n; i++)
                arr[i] = nextDouble();
            return arr;
        }
        public double[][] nextDoubleArray(int n, int m) throws IOException {
            double[][] arr = new double[n][m];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    arr[i][j] = nextDouble();
            return arr;
        }
        public char[][] nextCharArray(int n, int m) throws IOException {
            char[][] arr = new char[n][];
            for (int i = 0; i < n; i++)
                arr[i] = next().toCharArray();
            return arr;
        }
    }
}
