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 static java.lang.Integer.compare;
import static java.lang.Math.*;
import static java.lang.System.in;
import static java.lang.System.out;
import static java.util.Arrays.deepToString;

/**
 * 20/1/18
 * 9:01 PM
 *
 * @author remedy441
 */
public class CF914 {
    public static int mod = (int) (1e9 + 7);
    public static InputReader in;
    public static PrintWriter out;
    public static long ncr[][];

    public static void generateNcR(int N, int R){
        for(int i=0;i<=N;i++){
            for(int j=0;j<=i;j++){
                if(j==0||i==j){
                    ncr[i][j] = 1;
                }
                else{
                    ncr[i][j] = ncr[i-1][j-1]%mod + ncr[i-1][j]%mod;
                    ncr[i][j]%=mod;
                }
            }
        }
    }
    public static void solve() throws FileNotFoundException {


        in = new InputReader(System.in);
        out = new PrintWriter(System.out);
        ncr = new long[1001][1001];
        generateNcR(1000,1000);

        int time[] = new int[1001];
        time[1] = 0;
        for(int i=2;i<=1000;i++)
            time[i] = time[Integer.bitCount(i)]+1;

        String s = in.nextLine();
        int k = in.ni();

        if(k==0)
            out.println(1);
        else{
            long ans = 0;
            for(int i = 1;i<=1000;i++){
                if(time[i]!=k-1)
                    continue;
                int c = 0;
                for(int j=0;j<s.length();j++){
                    if(s.charAt(j)=='1'){
                        int on = i-c;
                        int pos = s.length()-j-1;
                        ans = ans%mod + nCr(pos,on)%mod;
                        ans%=mod;
                        c++;
                    }
                }
                if(i==1){
                    ans = (ans-1)%mod;
                }
                if(c==i)
                    ans = (ans+1)%mod;
            }
            out.println(ans);
        }

        out.close();
    }

    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) {
        new Thread(null, new Runnable() {
            public void run() {
                try {
                    solve();
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
        }, "1", 1 << 26).start();
    }

    static class Pair implements Comparable<Pair> {

        int x, y, i;

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

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

        public int compareTo(Pair o) {
            if (this.x != o.x)
                return compare(this.x, o.x);
            else
                return compare(this.y, o.y);
            //return 0;
        }

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

        public int hashCode() {
            return new Integer(x).hashCode() * 31 + new Integer(y).hashCode() + new Integer(i).hashCode() * 37;
        }

    }

    public static long add(long a, long b) {
        long x = (a + b);
        while (x >= mod)
            x -= mod;
        return x;
    }

    public static long sub(long a, long b) {
        long x = (a - b);
        while (x < 0)
            x += mod;
        return x;
    }

    public static long mul(long a, long b) {
        long x = (a * b);
        while (x >= mod)
            x -= mod;
        return x;
    }

    public static boolean isPal(String s) {
        for (int i = 0, j = s.length() - 1; i <= j; i++, j--) {
            if (s.charAt(i) != s.charAt(j))
                return false;
        }
        return true;
    }

    public static String rev(String s) {
        StringBuilder sb = new StringBuilder(s);
        sb.reverse();
        return sb.toString();
    }

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

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

    static int modInverse(int a, int m) {
        int m0 = m, t, q;
        int x0 = 0, x1 = 1;
        if (m == 1)
            return 0;
        while (a > 1) {
            // q is quotient
            q = a / m;
            t = m;
            // m is remainder now, process same as
            // Euclid's algo
            m = a % m;
            a = t;
            t = x0;
            x0 = x1 - q * x0;
            x1 = t;
        }
        // Make x1 positive
        if (x1 < 0)
            x1 += m0;
        return x1;
    }

    public static long gcdExtended(long a, long b, long[] x) {

        if (a == 0) {
            x[0] = 0;
            x[1] = 1;
            return b;
        }
        long[] y = new long[2];
        long gcd = gcdExtended(b % a, a, y);

        x[0] = y[1] - (b / a) * y[0];
        x[1] = y[0];

        return gcd;
    }

    public static long mulmod(long a, long b, long m) {
        if (m <= 1000000009)
            return a * b % m;

        long res = 0;
        while (a > 0) {
            if ((a & 1) != 0) {
                res += b;
                if (res >= m)
                    res -= m;
            }
            a >>= 1;
            b <<= 1;
            if (b >= m)
                b -= m;
        }
        return res;
    }

    public static int abs(int a, int b) {
        return (int) Math.abs(a - b);
    }

    public static long abs(long a, long b) {
        return (long) Math.abs(a - b);
    }

    public static int max(int a, int b) {
        if (a > b)
            return a;
        else
            return b;
    }

    public static int min(int a, int b) {
        if (a > b)
            return b;
        else
            return a;
    }

    public static long max(long a, long b) {
        if (a > b)
            return a;
        else
            return b;
    }

    public static long min(long a, long b) {
        if (a > b)
            return b;
        else
            return a;
    }

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

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

    public static void debug(Object... o) {
        System.out.println(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 ni() {
            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 nl() {
            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[] nIArr(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public long[] nLArr(int n) {
            long a[] = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nl();
            }
            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);
        }

    }
}