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:
/**
 p * @author prakhar28
 *
 */
import java.io.*;
import java.util.*;
import java.util.Map.Entry;
import java.text.*;
import java.math.*;
import java.util.regex.*;


import java.io.IOException;
import java.nio.file.Files;
import java.nio.file.Paths;

public class Main{
	
	static class Reader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
 
        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public String readLine() throws IOException
        {
            byte[] buf = new byte[200005]; // line length+1
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n' || c==' ') {
                	//buf[cnt++]=(byte)c;
                    break;
                }
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }
 
        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');
 
            if (neg)
                return -ret;
            return ret;
        }
 
        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
 
        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
 
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
 
            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }
 
            if (neg)
                return -ret;
            return ret;
        }
 
        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
 
        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
 
        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }
	
	static class FastScanner {

	    private final BufferedReader bufferedReader;
	    private StringTokenizer stringTokenizer;

	    public FastScanner() {
	        bufferedReader = new BufferedReader(new InputStreamReader(System.in));
	    }

	    public String next() {
	        while (stringTokenizer == null || !stringTokenizer.hasMoreElements()) {
	            try {
	                stringTokenizer = new StringTokenizer(bufferedReader.readLine());
	            } catch (IOException e) {
	                throw new RuntimeException("Can't read next value", e);
	            }
	        }
	        return stringTokenizer.nextToken();
	    }

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

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

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

	    public String nextLine(){
	        String str = "";
	        try {
	            str = bufferedReader.readLine();
	        } catch (IOException e) {
	            e.printStackTrace();
	        }
	        return str;
	    }
	}
	
	static void closeall() throws IOException{
		printWriter.close();
		sc.close();
		in.close();
	}
	static Scanner sc = new Scanner(System.in);
	static Reader in = new Reader();
	static FastScanner fastScanner = new FastScanner();
	static PrintWriter printWriter = new PrintWriter(new BufferedOutputStream(System.out));
	static BufferedReader read = new BufferedReader(new InputStreamReader(System.in));
	static long INF = (long)(1e18);

	
	int V,E;
	ArrayList<Integer> adj[];
	Main(int v){
		V=v;
		adj=new ArrayList[v];
		for(int i=0;i<v;i++)
			adj[i] = new ArrayList<>();
	}
	void addEdge(int u,int v){
		adj[u].add(v);
		adj[v].add(u);
	}
	
	
	static long power(long a,long k)
	{
		long m = 1000000007;
	    long ans=1;
	    long tmp=a%m;
	    while(k>0)
	    {
	        if(k%2==1)
	        	ans=ans*tmp%m;
	        tmp=tmp*tmp%m;
	        k>>=1;
	    }
	    return ans;
	}
	
	static class Pair implements Comparable<Pair>{
		int a,b;
		Pair(int a,int b){
			this.a=a;
			this.b=b;
		}
		public int compareTo(Pair ob){
			return this.b-ob.b;
		}
		
	}
	static int gcd(int a,int b) {
		if(a<b) {
			int t = a;
			a = b;
			b = t;
		}
		int r = a%b;
		if(r==0)
			return b;
		return gcd(b,r);
	}
	
	static int lower_bound(int[] a,int low,int high,int val) {
		while(low!=high) {
			int mid = (low+high)/2;
			if(a[mid]<val)
				low=mid+1;
			else
				high=mid;
		}
		return low;
	}
	
	static int max(int a,int b) {
		return (int)Math.max(a, b);
	}
	static long max(long a,long b) {
		return (long)Math.max(a, b);
	}
	static long min(long a,long b) {
		return (long)Math.min(a, b);
	}
	static int min(int a,int b) {
		if(a<b)
			return a;
		return b;
	}
	static long m = 1000000007;
	static long f[]; 
	static long inv[]; 
	
	Main(){
		f= new long[(int)1e6+5];
		inv= new long[(int)1e6+5];
		f[0]=1;
		for(int i=1;i<f.length;i++)
			f[i]=(f[i-1]*i)%m;
		inv[inv.length-1] = power(f[f.length-1],m - 2);
		for(int i = inv.length - 2; i >= 0; i--)  
			inv[i] = inv[i + 1]*(i + 1)%m;
	}
	
	static long C(int a,int b) {
		long s = ((f[a]%m)*(inv[b]%m)%m*(inv[a-b]%m))%m;
		return s;
	}
	public static void main(String args[])throws IOException{
		Main ob = new Main();
		int[] cnt = new int[1001];
		for(int i=1;i<=1000;i++) {
			int p = i;
			int c = 0;
			while(p>1) {
				while(p>0) {
					int r = p%2;
					c+=r;
					p/=2;
				}
				cnt[i]++;
				p=c;
				c=0;
			}
		}
		String s = read.readLine();
		int[] num = new int[s.length()];
		int sp=-1;
		for(int i=0;i<s.length();i++) {
			num[i]=s.charAt(i)-48;
			if(num[i]==1 && sp==-1){
				sp=s.length()-1-i;
			}
		}
		long ans = 0;
		int k = Integer.parseInt(read.readLine());
		if(k==0) {
			printWriter.println(1);
			closeall();
			return;
		}
		for(int i=1;i<=1000;i++) {
			if(cnt[i]==k-1) {
				ans=(ans%m+get(num,i)%m)%m;
				//printWriter.println(ans+" "+i);
			}
		}
		printWriter.println(ans);
		closeall();
	}
	
	static long get(int[] num,int k) {
		long ans = 0;
		int cnt = 0;
		for(int i=0;i<num.length;i++) {
			if(num[i]==0)
				continue;
			//len remaining = num.length-1-i
			//set remaining = k-cnt
			if(num.length-1-i<k-cnt || k-cnt<0)
				break;
			ans=(ans%m+C(num.length-1-i,k-cnt)%m)%m;
			cnt++;
			//System.out.println(cnt);
		}
		cnt=0;
		for(int i=0;i<num.length;i++) {
			if(num[i]==1)
				cnt++;
		}
		if(cnt==k)
			ans=(ans+1)%m;
		if(k==1 && ans>0)
			ans=(ans-1+m)%m;
		return ans;
	}
}