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.io.*;
import java.util.*;

import static java.math.BigDecimal.valueOf;

public class Main {
    static MyScanner sc;
    private static PrintWriter out;
    static long M2 = 1_000_000_000L + 7;

    public static void main(String[] s) throws Exception {
        StringBuilder stringBuilder = new StringBuilder();

//        stringBuilder.append("4 10 4 0 4 4 0 4 0 0");
//        stringBuilder.append("3 10\n" +
//                "3 1\n" +
//                "0 2\n" +
//                "5 3");
//        stringBuilder.append("110 2");
        if (stringBuilder.length() == 0) {
            sc = new MyScanner(System.in);
        } else {
            sc = new MyScanner(new BufferedReader(new StringReader(stringBuilder.toString())));
        }


        out = new PrintWriter(new OutputStreamWriter(System.out));
        initData();
        solve();
        out.flush();
    }


    private static void initData() {

    }


    private static void solve() throws IOException {
        String l = sc.next();
        int n = sc.nextInt();
        if (n == 0) {
            out.println(1);
            return;
        }
        if (n == 1) {
            out.println(l.length() - 1);
            return;
        }

        int[] r = new int[1020];
        for (int s = 2; s < r.length; s++) {
            int v = Integer.bitCount(s);
            r[s] = r[v] + 1;
        }

        long[][] xx = new long[1001][1001];
        for (int s = 0; s < xx.length; s++) {
            xx[s][0] = 1;
            for (int kk = 1; kk <= s; kk++) {
                xx[s][kk] = xx[s - 1][kk] + xx[s - 1][kk - 1];
                xx[s][kk] %= M2;
            }
        }

        int a = 0;
        long res = 0;
        for (int i = 0; i < l.length(); i++) {
            if (l.charAt(i) == '1') {
                int len = l.length() - i - 1;
                for (int k = 0; k <= len; k++) {
                    if (r[a + k] == n - 1) {
                        res += xx[len][k];
                        res %= M2;
                    }
                }
                a++;
            }
        }
        if (r[a] == n - 1) {
            res++;
        }

        out.println(res % M2);
    }

    private static int ccw(int[] i1, int[] i2) {
        return ccw(i1, i2, new int[]{0, 0});
    }

    private static int ccw(int[] s1, int[] s2, int[] right) {
        long xa = s1[0] - right[0];
        long xb = s1[1] - right[1];
        long ya = s2[0] - right[0];
        long yb = s2[1] - right[1];
        return Long.compare(xb * ya, xa * yb);
    }


    private static void solveT() throws IOException {
        int t = sc.nextInt();
        while (t-- > 0) {
            solve();
        }
    }

    private static long gcd(long l, long l1) {
        if (l > l1) return gcd(l1, l);
        if (l == 0) return l1;
        return gcd(l1 % l, l);
    }

    private static long pow(long a, long b, long m) {
        if (b == 0) return 1;
        if (b == 1) return a;
        long pp = pow(a, b / 2, m);
        pp *= pp;
        pp %= m;
        return (pp * (b % 2 == 0 ? 1 : a)) % m;
    }


    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        MyScanner(BufferedReader br) {
            this.br = br;
        }

        public MyScanner(InputStream in) {
            this(new BufferedReader(new InputStreamReader(in)));
        }

        void findToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
        }

        String next() {
            findToken();
            return st.nextToken();
        }

        Integer[] nab(int n) {
            Integer[] k = new Integer[n];
            for (int i = 0; i < n; i++) {
                k[i] = sc.fi();
            }
            return k;
        }

        int[] na(int n) {
            int[] k = new int[n];
            for (int i = 0; i < n; i++) {
                k[i] = sc.fi();
            }
            return k;
        }

        long[] nl(int n) {
            long[] k = new long[n];
            for (int i = 0; i < n; i++) {
                k[i] = sc.nextLong();
            }
            return k;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int fi() {
            String t = next();
            int cur = 0;
            boolean n = t.charAt(0) == '-';
            for (int a = n ? 1 : 0; a < t.length(); a++) {
                cur = cur * 10 + t.charAt(a) - '0';
            }
            return n ? -cur : cur;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }


}