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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class CFC {

    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;
    final long MOD = 1000L * 1000L * 1000L + 7;
    int[] dx = {0, -1, 0, 1};
    int[] dy = {1, 0, -1, 0};

    long[][] comb;
    int m = 1005;
    int[] steps;
    void solve() throws IOException {
        String str = nextString();
        int k = nextInt();

        if (k == 0) {
            if (str.equals("0")) {
                out(0);
            }
            else {
                out(1);
            }
            return;
        }

        comb = new long[m][m];
        for (int i = 0; i < m; i++) {
            comb[i][i] = 1;
            comb[i][0] = 1;
        }
        for (int i = 2; i < m; i++) {
            for (int j = 1; j < i; j++) {
                comb[i][j] = comb[i - 1][j - 1] + comb[i - 1][j];
                comb[i][j] %= MOD;
            }
        }

        steps = new int[m];
        steps[0] = m - 1;
        for (int i = 2; i < m; i++) {
            int bits = Integer.bitCount(i);
            steps[i] = steps[bits] + 1;
        }

        List<List<Integer>> map = new ArrayList<>();
        for (int i = 0; i < m; i++) {
            map.add(new ArrayList<>());
        }
        for (int i = 0; i < m; i++) {
            map.get(steps[i]).add(i);
        }

        long res = 0;
        if (getStep(str) == k) {
            res++;
        }

        int len = str.length();
        for (int i = 0; i < len; i++) {
            if (str.charAt(i) == '1') {
                int one = 0;
                for (int j = 0; j < i; j++) {
                    if (str.charAt(j) == '1') {
                        one++;
                    }
                }

                int left = len - 1 - (i + 1) + 1;
                List<Integer> cnts = map.get(k - 1);
                for (int v : cnts) {
                    int need = v - one;
                    if (need < 0) {
                        continue;
                    }
                    long add = comb[left][need];
                    if (need == 1 && one == 0) {
                        add = Math.max(0, add - 1);
                    }

                    res += add;
                    res %= MOD;
                }
            }
        }

        out(res % MOD);
    }

    int getStep(int value) {
        if (value == 1) {
            return 0;
        }

        return 1 + getStep(Integer.bitCount(value));
    }

    int getStep(String str) {
        if (str.equals("1")) {
            return 0;
        }

        int cnt = 0;
        for (int i = 0; i < str.length(); i++) {
            if (str.charAt(i) == '1') {
                cnt++;
            }
        }

        return getStep(cnt) + 1;
    }

    void shuffle(int[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            int tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }

    int gcd(int a, int b) {
        while(a != 0 && b != 0) {
            int c = b;
            b = a % b;
            a = c;
        }
        return a + b;
    }
    private void outln(Object o) {
        out.println(o);
    }
    private void out(Object o) {
        out.print(o);
    }
    public CFC() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }
    public static void main(String[] args) throws IOException {
        new CFC();
    }

    public long[] nextLongArr(int n) throws IOException{
        long[] res = new long[n];
        for(int i = 0; i < n; i++)
            res[i] = nextLong();
        return res;
    }
    public int[] nextIntArr(int n) throws IOException {
        int[] res = new int[n];
        for(int i = 0; i < n; i++)
            res[i] = nextInt();
        return res;
    }
    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }
    public String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}