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 java.math.*;
import java.lang.*;
 
import static java.lang.Math.*;
 
public class Main implements Runnable
{
	static class InputReader
	{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		private BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
 
		public InputReader(InputStream stream)
		{
			this.stream = stream;
		}
		
		public int read()
		{
			if (numChars==-1) 
				throw new InputMismatchException();
			
			if (curChar >= numChars)
			{
				curChar = 0;
				try 
				{
					numChars = stream.read(buf);
				}
				catch (IOException e)
				{
					throw new InputMismatchException();
				}
				
				if(numChars <= 0)				
					return -1;
			}
			return buf[curChar++];
		}
	 
		public String nextLine()
		{
			String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
		}
		public int nextInt()
		{
			int c = read();
			
			while(isSpaceChar(c)) 
				c = read();
			
			int sgn = 1;
			
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			
			int res = 0;
			do 
			{
				if(c<'0'||c>'9') 
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			while (!isSpaceChar(c)); 
			
			return res * sgn;
		}
		
		public long nextLong() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			long res = 0;
			
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			while (!isSpaceChar(c));
				return res * sgn;
		}
		
		public double nextDouble() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') 
			{
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, nextInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') 
			{
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) 
				{
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, nextInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
		
		public String readString() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isSpaceChar(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;
		}
	 
		public String next() 
		{
			return readString();
		}
		
		public interface SpaceCharFilter 
		{
			public boolean isSpaceChar(int ch);
		}
	}
 	
	public static void main(String args[]) throws Exception
	{
		new Thread(null, new Main(),"Main",1<<26).start();
	}
	int bitCount(int i) { 
		i = i - ((i >>> 1) & 0x55555555); 
		i = (i & 0x33333333) + ((i >>> 2) & 0x33333333); 
		i = (i + (i >>> 4)) & 0x0f0f0f0f; 
		i = i + (i >>> 8); 
		i = i + (i >>> 16); 
		return i & 0x3f; 
	}
	long fast_pow(long a, long b) {
		if(b == 0)
			return 1;
		long val = fast_pow(a, b / 2);
		if(b % 2 == 0)
			return val * val % mod;
		else
			return val * val % mod * a % mod;
	}
	long getComb(int n, int r) {
		return fact[n] * factinv[r] % mod * factinv[n - r] % mod;
	}
	long mod = (long)1e9 + 7;
	long fact[];
	long factinv[];
	public void run()
	{
		InputReader sc = new InputReader(System.in);
		PrintWriter w = new PrintWriter(System.out);

		char s[] = sc.next().toCharArray();
		long ans = 0;
		int alrbits = 0;
		int k = sc.nextInt();

		if(k == 0) {
			w.print("1");
			w.close();
			return;
		}
		else if(k == 1) {
			w.print(s.length - 1);
			w.close();
			return;
		}

		int dp[] = new int[1001];


		dp[0] = 1000000;
		for(int i = 1; i <= 1000; ++i) {
			int temp = i;
			while(temp != 1) {
				dp[i]++;
				temp = bitCount(temp);
			}
		}

		fact = new long[1001];
		factinv = new long[1001];

		fact[0] = 1;
		factinv[0] = fast_pow(fact[0], mod - 2);

		for(int i = 1; i <= 1000; ++i) {
			fact[i] = fact[i - 1] * i % mod;
			factinv[i] = fast_pow(fact[i], mod - 2);
		}

		int leftBits = 0;

		for(int i = 0; i < s.length; ++i) {
			if(s[i] == '1') {
				int maxBits = s.length - 1 - i;
				for(int j = 0; j <= maxBits; ++j) {
					if(dp[j + alrbits] == k - 1) {
						ans = (ans + getComb(maxBits, j)) % mod;
					}
				}
				alrbits++;
			}
		}

		if(dp[alrbits] == k - 1)
			ans = (ans + 1) % mod;

		w.print(ans);

		w.close();	
   	}
}