Problem: The Travelling Salesman spends a lot of time travelling so he tends to get bored. To pass time, he likes to perform operations on numbers. One such operation is to take a positive integer x and reduce it to the number of bits set to 1 in the binary representation of x. For example for number 13 it's true that 1310 = 11012, so it has 3 bits set and 13 will be reduced to 3 in one operation.

He calls a number special if the minimum number of operations to reduce it to 1 is k.

He wants to find out how many special numbers exist which are not greater than n. Please help the Travelling Salesman, as he is about to reach his destination!

Since the answer can be large, output it modulo 109 + 7.

Input

The first line contains integer n (1 ≤ n < 21000).

The second line contains integer k (0 ≤ k ≤ 1000).

Note that n is given in its binary representation without any leading zeros.

Output

Output a single integer — the number of special numbers not greater than n, modulo 109 + 7.

Examples

Input

110
2


Output

3


Input

111111011
2


Output

169

Note

In the first sample, the three special numbers are 3, 5 and 6. They get reduced to 2 in one operation (since there are two set bits in each of 3, 5 and 6) and then to 1 in one more operation (since there is only one set bit in 2).

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.BigInteger;

public class MainE
{

    static int mod = (int) (1e9+7);
    static InputReader in;
    static PrintWriter out;
    static long[][] nCr;

    static void choose(int maxN, int maxR) {
        nCr = new long[maxN + 1][maxR + 1];
        for (int i = 0; i <= maxN; i++) {
            for (int j = 0; j <= i; j++) {
                if (j == 0 || j == i || i == 0) {
                    nCr[i][j] = 1;
                } else {
                    nCr[i][j] = (nCr[i - 1][j - 1] + nCr[i - 1][j]) % mod;
                }
            }
        }
    }

    static long nCr(int n, int r) {
        if (n == r) {
            return 1;
        }
        if (n < 0 || r < 0) {
            return 0;
        }
        return nCr[n][r];
    }

    public static void main(String[] args)
    {
        in = new InputReader(System.in);
        out = new PrintWriter(System.out);            
        
        int t = 1;
        while(t-- > 0){
            int maxn = 1005;
            int[] time = new int[maxn];
            time[1] = 0;
            for(int i = 2; i < maxn; i++){
                time[i] = time[Integer.bitCount(i)] + 1;
            }
            nCr = new long[maxn][maxn];
            choose(maxn, maxn);
            String s = in.readString();
            int k = in.nextInt();
            if(k == 0){
                out.println(1);
                continue;
            }
            long res = 0;
            for(int i = 1; i < maxn; i++){
                if(time[i] != k - 1) continue;
                int c = 0;
                for(int j = 0; j < s.length(); j++){
                    if(s.charAt(j) == '1'){
                        res = (res + nCr(s.length() - j - 1, i - c)) % mod;
                        c++;
                    }
                   // debug(res);
                }
                if(i == 1) res = (res - 1) % mod;
                if(c == i) res = (res + 1) % mod;
            }
            
            out.println(res);
        }
        out.close(); 
    }
    
    static class Pair implements Comparable<Pair>
    {

        int x,y;
        int i;
        
        Pair (int x,int y)
        {
                this.x = x;
                this.y = y;
        }

        Pair (int x,int y, int i)
        {
                this.x = x;
                this.y = y;
                this.i = i;
        }

        public int compareTo(Pair o)
        {
            return Long.compare(this.x,o.x);
                //return 0;
        }

        public boolean equals(Object o)
        {
            if (o instanceof Pair)
            {
                Pair p = (Pair)o;
                return p.x == x && p.y==y;
            }
            return false;
        }

        @Override
        public String toString()
        {
            return x + " "+ y + " "+i;
        }

        /*public int hashCode()
        {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode();
        }*/

    } 

    static long gcd(long x,long y)
    {
        if(y==0)
                return x;
        else
                return gcd(y,x%y);
    }

    static int gcd(int x,int y)
    {
        if(y==0)
                return x;
        else 
                return gcd(y,x%y);
    }

    static long pow(long n,long p,long m)
    {
         long  result = 1;
          if(p==0){
            return 1;
          }
          
        while(p!=0)
        {
            if(p%2==1)
                result *= n;
            if(result >= m)
               result %= m;
            p >>=1;
            n*=n;
            if(n >= m)
                n%=m;
        }
        
        return result;
    }

    static long pow(long n,long p)
    {
        long  result = 1;
          if(p==0)
            return 1;

        while(p!=0)
        {
            if(p%2==1)
                result *= n;	    
            p >>=1;
            n*=n;	    
        }
        return result;
    }

    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 long[] nextLongArray(int n)
        {
                long a[] = new long[n];
                for (int i = 0; i < n; i++)
                {
                        a[i] = nextLong();
                }
                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);
        }

    }
}