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.util.*;
import java.io.*;
import java.util.Queue;
import java.util.LinkedList;
import java.math.*;
 
     public class Sample implements Runnable
    { 
        
          static long[][] number=new long[1001][1001];
          public  static void solve()
          {  
              call();
              String n=s();
              int k=i();
              if(k==0){
                out.println("1");
                return;
              }

              long[] dp=new long[1001];
              dp[1]=0;
              for(int i=2;i<=1000;i++)dp[i]=dp[count_one(i)]+1;

              int niche=0;
              long ans=0;
              for(int i=0;i<n.length();i++)
              {
                if(n.charAt(i)=='0')continue;
                else
                {
                  for(int j=Math.max(niche,1);j<1000;j++)
                  {
                    if(dp[j]==k-1){
                        ans=(ans+number[n.length()-i-1][j-niche]);
                        if(i==0 && k==1)
                        {
                          ans=(mod+ans-1)%mod;
                        }
                    }
                  }
                }
                niche++;

              }
              int count=0;
              for(int i=0;i<n.length();i++)
              {
                if(n.charAt(i)=='1')count++;
              }
              if(dp[count]==k-1)ans=(ans+1)%mod;

              out.println(ans%mod);

                        
          }
          public static void call(){
              for(int i=0;i<=1000;i++)
              {
                number[i][0]=1;
              }
              for(int i=1;i<=1000;i++)
              {
                for(int j=1;j<=1000;j++)
                {
                    number[i][j]=(number[i-1][j]+number[i-1][j-1])%mod;
                }
              }

          }
          public static int count_one(int n)
          {
            int count=0;
            while(n>0)
            {
                if(n%2==1)count++;
                n/=2;
            }
            return count;

          }
          
          
           
           
          public void run()
          {   
              solve();
              out.close();
          }
 
          public static void main(String[] args) throws IOException
          { 
                new Thread(null, new Sample(), "whatever", 1<<26).start();
          }
         abstract static class Pair implements Comparable<Pair>
         {
            long a;
            int b;
            
            Pair(){}
            Pair(long a,int b)
            {
                       this.a=a;
                       this.b=b;
            }
   
            public int compareTo(Pair x)
           {
                return Long.compare(x.a,this.a);
           }
        }
        
       
         
    ////////////////////////////////////////////////////// Merge Sort ////////////////////////////////////////////////////////////////////////
     
   static class Merge 
   {
 
        public static void sort(long inputArr[]) 
        {
            int length = inputArr.length;
            doMergeSort(inputArr,0, length - 1);
        }
 
        private static void doMergeSort(long[] arr,int lowerIndex, int higherIndex) 
        {        
            if (lowerIndex < higherIndex) {
                int middle = lowerIndex + (higherIndex - lowerIndex) / 2;
                doMergeSort(arr,lowerIndex, middle);
                doMergeSort(arr,middle + 1, higherIndex);
                mergeParts(arr,lowerIndex, middle, higherIndex);
            }
        }
 
        private static void mergeParts(long[]array,int lowerIndex, int middle, int higherIndex) 
        {
            long[] temp=new long[higherIndex-lowerIndex+1];
            for (int i = lowerIndex; i <= higherIndex; i++) 
            {
                temp[i-lowerIndex] = array[i];
            }
            int i = lowerIndex;
            int j = middle + 1;
            int k = lowerIndex;
            while (i <= middle && j <= higherIndex) 
            {
                if (temp[i-lowerIndex] < temp[j-lowerIndex]) 
                {
                    array[k] = temp[i-lowerIndex];
                    i++;
                } else {
                    array[k] = temp[j-lowerIndex];
                    j++;
                }
                k++;
            }
            while (i <= middle) 
            {
                array[k] = temp[i-lowerIndex];
                k++;
                i++;
            }
            while(j<=higherIndex)
            {
                array[k]=temp[j-lowerIndex];
                k++;
                j++;
            }
        }
 
    }
        
      
    /////////////////////////////////////////////////////////// Methods ////////////////////////////////////////////////////////////////////////
 
 
     static boolean isPal(String s)
     {
        for(int i=0, j=s.length()-1;i<=j;i++,j--)
        {
                if(s.charAt(i)!=s.charAt(j)) return false;
        }
        return true;
     }
     static String rev(String s)
     {
                StringBuilder sb=new StringBuilder(s);
                sb.reverse();
                return sb.toString();
     }
     static int gcd(int a,int b){return (a==0)?b:gcd(b%a,a);}
     static long gcdExtended(long a,long b,long[] x)
     {
 
        if(a==0){
            x[0]=0;
            x[1]=1;
            return b;
        }
        long[] y=new long[2];
        long gcd=gcdExtended(b%a, a, y);
 
        x[0]=y[1]-(b/a)*y[0];
        x[1]=y[0];
 
        return gcd;
    }
 
     boolean findSum(int set[], int n, long sum)
    {
      if (sum == 0)
         return true;
      if (n == 0 && sum != 0)
         return false;
      if (set[n-1] > sum)
         return findSum(set, n-1, sum);
      return findSum(set, n-1, sum) ||findSum(set, n-1, sum-set[n-1]);
    }
   
      public static long modPow(long base, long exp, long mod)
     {
        base = base % mod;
        long result = 1;
        while (exp > 0)
       {
            if (exp % 2 == 1) 
            {
                result = (result * base) % mod;
            }
            base = (base * base) % mod;
            exp = exp >> 1;
       }
        return result;
    }
 
    static long[] fac;
    static long[] inv;
    static long mod=(long)1e9+7;
    public static void cal() 
    {
        fac = new long[1000005];
        inv = new long[1000005];
        fac[0] = 1;
        inv[0] = 1;
        for (int i = 1; i <= 1000000; i++)
        {
            fac[i] = (fac[i - 1] * i) % mod;
            inv[i] = (inv[i - 1] * modPow(i, mod - 2, mod)) % mod;
        }
    }
 
    public static long ncr(int n, int r) 
    {
        return (((fac[n] * inv[r]) % mod) * inv[n - r]) % mod;
    }
 
 
////////////////////////////////////////// Input Reader ////////////////////////////////////////////////////////////////////////////////////////////////////
     
    static InputReader sc = new InputReader(System.in);
    static PrintWriter out= new PrintWriter(System.out);   
    
    static class InputReader {
 
          private final InputStream stream;
          private final byte[] buf = new byte[8192];
          private int curChar, snumChars;
          private SpaceCharFilter filter;
 
          public InputReader(InputStream stream) {
                  this.stream = stream;
          }
 
          public int snext()
         {
                  if (snumChars == -1)
                          throw new InputMismatchException();
                  if (curChar >= snumChars) {
                          curChar = 0;
                          try {
                                  snumChars = stream.read(buf);
                          } catch (IOException e) {
                                  throw new InputMismatchException();
                          }
                          if (snumChars <= 0)
                                  return -1;
                  }
                  return buf[curChar++];
          }
 
          public int nextInt()
         {
                  int c = snext();
                  while (isSpaceChar(c)) 
                  {
                          c = snext();
                  }
                  int sgn = 1;
                  if (c == '-')
                  {
                          sgn = -1;
                          c = snext();
                  }
                  int res = 0;
                  do {
                          if (c < '0' || c > '9')
                                  throw new InputMismatchException();
                          res *= 10;
                          res += c - '0';
                          c = snext();
                  } while (!isSpaceChar(c));
                  return res * sgn;
          }
 
          public long nextLong() 
          {
                  int c = snext();
                  while (isSpaceChar(c)) 
                  {
                          c = snext();
                  }
                  int sgn = 1;
                  if (c == '-') 
                  {
                          sgn = -1;
                          c = snext();
                  }
                  long res = 0;
                  do {
                          if (c < '0' || c > '9')
                                  throw new InputMismatchException();
                          res *= 10;
                          res += c - '0';
                          c = snext();
                  } while (!isSpaceChar(c));
                  return res * sgn;
          }
 
          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 String nextLine()
         {
                  int c = snext();
                  while (isSpaceChar(c))
                          c = snext();
                  StringBuilder res = new StringBuilder();
                  do {
                          res.appendCodePoint(c);
                          c = snext();
                  } while (!isEndOfLine(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;
          }
 
          private boolean isEndOfLine(int c) 
          {
                  return c == '\n' || c == '\r' || c == -1;
          }
 
          public interface SpaceCharFilter 
          {
                  public boolean isSpaceChar(int ch);
          }
 
    }
 
    static int i()
    {
        return sc.nextInt();
    }
    static long l(){
        return sc.nextLong();
    }
    static int[] iarr(int n)
    {
        return sc.nextIntArray(n);
    }
    static long[] larr(int n)
    {
        return sc.nextLongArray(n);
    }
    static String s(){
        return sc.nextLine();
    }
  
 
 }