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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;

public class Main {

	static PrintWriter out;
	static InputReader ir;

	static void solve() {
		char[] s = ir.next().toCharArray();
		int k = ir.nextInt();
		if(k==0){
			out.println(1);
			return;
		}
		if(k==1){
			out.println(s.length-1);
			return;
		}
		long mod = (long) 1e9 + 7, ret = 0;
		int[] dp = new int[1001];
		long[] fact=factArray(1100,mod);
		long[] factInv=factInverseArray(1100,mod);
		for (int i = 2; i <= 1000; i++) {
			dp[i] = dp[Integer.bitCount(i)] + 1;
			if (dp[i]+1 == k&&i<=s.length) {
				ret += calc(s, 0,0, i, mod,fact,factInv);
				ret %= mod;
			}
		}
		out.println(ret);
	}

	public static long mod_inverse(long a, long MOD) {
		long[] ret = extgcd(a, MOD);
		return (MOD + ret[0] % MOD) % MOD;
	}

	public static long[] extgcd(long a, long b) {
		long[] ret = new long[3];
		ret[2] = _extgcd(a, b, ret);
		return ret;
	}

	private static long _extgcd(long a, long b, long[] x) {
		long g = a;
		x[0] = 1;
		x[1] = 0;
		if (b != 0) {
			g = _extgcd(b, a % b, x);
			long temp = x[0];
			x[0] = x[1];
			x[1] = temp;
			x[1] -= (a / b) * x[0];
		}
		return g;
	}

	private static long[] factArray(int n, long MOD) {
		long[] ret = new long[n + 1];
		ret[0] = 1 % MOD;
		for (int i = 1; i <= n; i++) {
			ret[i] = ret[i - 1] * i;
			ret[i] %= MOD;
		}
		return ret;
	}

	private static long[] factInverseArray(int n, long MOD) {
		long[] ret = new long[n + 1];
		ret[0] = 1;
		for (int i = 1; i <= n; i++) {
			ret[i] = ret[i - 1] * mod_inverse((long) i, MOD) % MOD;
		}
		return ret;
	}

	public static long comb(int n, int m, long[] fact, long[] factInv, long MOD) {
		long ret = fact[n];
		ret *= factInv[m];
		ret %= MOD;
		ret *= factInv[n - m];
		ret %= MOD;
		return ret;
	}

	static long calc(char[] s,int cur,int idx,int len,long mod,long[] fact,long[] factInv){
		if(cur==len)
			return 1;
		int p=idx;
		while(p<s.length&&s[p]=='0')
			p++;
		if(p>=s.length)
			return 0;
		int f=s.length-p-1;
		long ret=0;
		if(f>=len-cur)
			ret+=comb(f,len-cur,fact,factInv,mod);
		ret%=mod;
		if(f>=len-cur-1)
			ret+=calc(s,cur+1,p+1,len,mod,fact,factInv);
		return ret%mod;
	}

	public static void main(String[] args) throws Exception {
		ir = new InputReader(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.flush();
	}

	static class InputReader {

		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;

		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}

		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}

		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}

		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}

		public boolean hasNext() {
			skip();
			return hasNextByte();
		}

		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}

		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}

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

		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 char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
}