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 com.sun.jmx.snmp.BerEncoder;
import com.sun.org.apache.regexp.internal.RE;

import java.io.*;
import java.nio.file.ClosedWatchServiceException;
import java.nio.file.OpenOption;
import java.security.SecureRandom;
import java.util.*;

public class Main {
    public static void main(String[] args) throws FileNotFoundException {
        ConsoleIO io = new ConsoleIO(new InputStreamReader(System.in), new PrintWriter(System.out));
        //String test = "C-large";
        //ConsoleIO io = new ConsoleIO(new FileReader("D:\\Dropbox\\code\\practice\\jb\\src\\" + test + ".in"), new PrintWriter(new File("D:\\Dropbox\\code\\practice\\jb\\src\\" + test + "-out.txt")));

        new Main(io).solve();

        io.close();
    }

    ConsoleIO io;
    Main(ConsoleIO io) {
        this.io = io;
    }

    List<List<Integer>> gr = new ArrayList<>();
    long MOD = 1_000_000_007;

    public void solve() {
        char[] s = io.readLine().toCharArray();
        int k = Integer.parseInt(io.readLine());

        if (k == 0) {
            io.writeLine("1");
            return;
        }
        if (k == 1) {
            io.writeLine((s.length - 1) + "");
            return;
        }

        List<Integer> can = new ArrayList<>();
        int[] steps = new int[1003];
        for (int i = 2; i < steps.length; i++) {
            int t = i;
            int q = 0;
            while (t > 0) {
                q += t % 2;
                t /= 2;
            }
            steps[i] = steps[q] + 1;
            if (steps[i] == k - 1)
                can.add(i);
        }


        fact = new long[1003];
        fact[0] = 1;
        for (int i = 1; i < fact.length; i++) {
            fact[i] = (fact[i - 1] * i) % MOD;
        }

        int ones = 0;
        for (int i = 0; i < s.length; i++)
            ones += s[i] - '0';

        long res = 0;
        for (int q = 0; q < can.size(); q++) {
            int t = can.get(q);
            if (t <= ones)
                res = (res + 1) % MOD;

            for (int i = 0; i < s.length && s.length - i - 1 >= t && t > 0; i++) {
                if (s[i] == '1') {
                    res += choose(s.length - i - 1, t);
                    res %= MOD;
                    t--;
                }
            }
        }

        io.writeLine(res + "");
    }

    long[] fact;

    private long choose(int n, int k){
        long den = fact[n-k] * fact[k] % MOD;
        return div(fact[n], den, MOD);
    }

    long div(long a, long b, long mod) {
        return (a * pow(b, mod - 2, mod)) % mod;
    }

    long pow(long a, long p, long mod) {
        long res = 1;
        while (p > 0) {
            if (p % 2 == 1) res = (res * a) % mod;
            a = (a * a) % mod;
            p /= 2;
        }
        return res;
    }



}

class ConsoleIO {

    BufferedReader br;
    PrintWriter out;
    public ConsoleIO(Reader reader, PrintWriter writer){br = new BufferedReader(reader);out = writer;}
    public void flush(){this.out.flush();}
    public void close(){this.out.close();}
    public void writeLine(String s) {this.out.println(s);}
    public void writeInt(int a) {this.out.print(a);this.out.print(' ');}
    public void writeWord(String s){
        this.out.print(s);
    }
    public void writeIntArray(int[] a, int k, String separator) {
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < k; i++) {
            if (i > 0) sb.append(separator);
            sb.append(a[i]);
        }
        this.writeLine(sb.toString());
    }
    public int read(char[] buf, int len){try {return br.read(buf,0,len);}catch (Exception ex){ return -1; }}
    public String readLine() {try {return br.readLine();}catch (Exception ex){ return "";}}
    public long[] readLongArray() {
        String[]n=this.readLine().trim().split("\\s+");long[]r=new long[n.length];
        for(int i=0;i<n.length;i++)r[i]=Long.parseLong(n[i]);
        return r;
    }
    public int[] readIntArray() {
        String[]n=this.readLine().trim().split("\\s+");int[]r=new int[n.length];
        for(int i=0;i<n.length;i++)r[i]=Integer.parseInt(n[i]);
        return r;
    }
    public int[] readIntArray(int n) {
        int[] res = new int[n];
        char[] all = this.readLine().toCharArray();
        int cur = 0;boolean have = false;
        int k = 0;
        boolean neg = false;
        for(int i = 0;i<all.length;i++){
            if(all[i]>='0' && all[i]<='9'){
                cur = cur*10+all[i]-'0';
                have = true;
            }else if(all[i]=='-') {
                neg = true;
            }
            else if(have){
                res[k++] = neg?-cur:cur;
                cur = 0;
                have = false;
                neg = false;
            }
        }
        if(have)res[k++] = neg?-cur:cur;
        return res;
    }
    public int ri() {
        try {
            int r = 0;
            boolean start = false;
            boolean neg = false;
            while (true) {
                int c = br.read();
                if (c >= '0' && c <= '9') {
                    r = r * 10 + c - '0';
                    start = true;
                } else if (!start && c == '-') {
                    start = true;
                    neg = true;
                } else if (start || c == -1) return neg ? -r : r;
            }
        } catch (Exception ex) {
            return -1;
        }
    }
    public long readLong() {
        try {
            long r = 0;
            boolean start = false;
            boolean neg = false;
            while (true) {
                int c = br.read();
                if (c >= '0' && c <= '9') {
                    r = r * 10 + c - '0';
                    start = true;
                } else if (!start && c == '-') {
                    start = true;
                    neg = true;
                } else if (start || c == -1) return neg ? -r : r;
            }
        } catch (Exception ex) {
            return -1;
        }
    }
    public String readWord() {
        try {
            boolean start = false;
            StringBuilder sb = new StringBuilder();
            while (true) {
                int c = br.read();
                if (c!= ' ' && c!= '\r' && c!='\n' && c!='\t') {
                    sb.append((char)c);
                    start = true;
                } else if (start || c == -1) return sb.toString();
            }
        } catch (Exception ex) {
            return "";
        }
    }
    public char readSymbol() {
        try {
            while (true) {
                int c = br.read();
                if (c != ' ' && c != '\r' && c != '\n' && c != '\t') {
                    return (char) c;
                }
            }
        } catch (Exception ex) {
            return 0;
        }
    }
    //public char readChar(){try {return (char)br.read();}catch (Exception ex){ return 0; }}
}
class Pair {
    public Pair(int a, int b) {this.a = a;this.b = b;}
    public int a;
    public int b;
}
class PairLL {
    public PairLL(long a, long b) {this.a = a;this.b = b;}
    public long a;
    public long b;
}
class Triple {
    public Triple(int a, int b, int c) {this.a = a;this.b = b;this.c = c;}
    public int a;
    public int b;
    public int c;
}