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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
namespace {
using Integer = long long;
template <class T, class S>
istream& operator>>(istream& is, pair<T, S>& p) {
  return is >> p.first >> p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& vec) {
  for (T& val : vec) is >> val;
  return is;
}
template <class T>
istream& operator,(istream& is, T& val) {
  return is >> val;
}
template <class T, class S>
ostream& operator<<(ostream& os, const pair<T, S>& p) {
  return os << p.first << " " << p.second;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& vec) {
  for (size_t i = 0; i < vec.size(); i++)
    os << vec[i] << (i == vec.size() - 1 ? "" : " ");
  return os;
}
template <class T>
ostream& operator,(ostream& os, const T& val) {
  return os << " " << val;
}
template <class H>
void print(const H& head) {
  cout << head;
}
template <class H, class... T>
void print(const H& head, const T&... tail) {
  cout << head << " ";
  print(tail...);
}
template <class... T>
void println(const T&... values) {
  print(values...);
  cout << endl;
}
template <class H>
void eprint(const H& head) {
  cerr << head;
}
template <class H, class... T>
void eprint(const H& head, const T&... tail) {
  cerr << head << " ";
  eprint(tail...);
}
template <class... T>
void eprintln(const T&... values) {
  eprint(values...);
  cerr << endl;
}
class range {
  Integer start_, end_, step_;

 public:
  struct range_iterator {
    Integer val, step_;
    range_iterator(Integer v, Integer step) : val(v), step_(step) {}
    Integer operator*() { return val; }
    void operator++() { val += step_; }
    bool operator!=(range_iterator& x) {
      return step_ > 0 ? val < x.val : val > x.val;
    }
  };
  range(Integer len) : start_(0), end_(len), step_(1) {}
  range(Integer start, Integer end) : start_(start), end_(end), step_(1) {}
  range(Integer start, Integer end, Integer step)
      : start_(start), end_(end), step_(step) {}
  range_iterator begin() { return range_iterator(start_, step_); }
  range_iterator end() { return range_iterator(end_, step_); }
};
inline string operator"" _s(const char* str, size_t size) {
  return move(string(str));
}
constexpr Integer my_pow(Integer x, Integer k, Integer z = 1) {
  return k == 0    ? z
         : k == 1  ? z * x
         : (k & 1) ? my_pow(x * x, k >> 1, z * x)
                   : my_pow(x * x, k >> 1, z);
}
constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z = 1) {
  return k == 0    ? z % M
         : k == 1  ? z * x % M
         : (k & 1) ? my_pow_mod(x * x % M, k >> 1, M, z * x % M)
                   : my_pow_mod(x * x % M, k >> 1, M, z);
}
constexpr unsigned long long operator"" _ten(unsigned long long value) {
  return my_pow(10, value);
}
inline int k_bit(Integer x, int k) { return (x >> k) & 1; }
mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(
               chrono::steady_clock::now().time_since_epoch())
               .count());
template <class T>
string join(const vector<T>& v, const string& sep) {
  stringstream ss;
  for (size_t i = 0; i < v.size(); i++) {
    if (i > 0) ss << sep;
    ss << v[i];
  }
  return ss.str();
}
inline string operator*(string s, int k) {
  string ret;
  while (k) {
    if (k & 1) ret += s;
    s += s;
    k >>= 1;
  }
  return ret;
}
}  // namespace
constexpr long long mod = 9_ten + 7;
long long check(string s, int k) {
  long long val = 0;
  for (int i = 0; i < s.size(); i++) {
    val = val * 2 + s[i] - '0';
  }
  long long ans = 0;
  for (int i = 1; i <= val; i++) {
    int tmp = i;
    int d = 0;
    while (tmp != 1) {
      tmp = __builtin_popcount(tmp);
      d++;
    }
    if (d == k) {
      ans++;
    }
  }
  return ans;
}
int main() {
  string s;
  cin >> s;
  int w;
  cin >> w;
  int n = s.size();
  vector<int> d(1001, -1);
  d[1] = 0;
  for (int i = 2; i <= 1000; i++) {
    int j = __builtin_popcount(i);
    d[i] = d[j] + 1;
  }
  vector<vector<long long>> dp(2, vector<long long>(n + 1, 0));
  dp[0][0] = 1;
  for (int i = 0; i < n; i++) {
    vector<vector<long long>> dp_(2, vector<long long>(n + 1, 0));
    int b = s[i] - '0';
    for (int k = 0; k < 2; k++) {
      for (int j = 0; j <= n; j++) {
        if (dp[k][j] == 0) continue;
        for (int x = 0; x <= 1; x++) {
          int j_ = j + x;
          int k_ = k | (b > x);
          if (k == 0 && b < x) continue;
          (dp_[k_][j_] += dp[k][j]) %= mod;
        }
      }
    }
    swap(dp, dp_);
  }
  long long ans = 0;
  if (w != 0) {
    for (int i = 0; i <= n; i++) {
      if (d[i] != w - 1) continue;
      for (int k = 0; k <= 1; k++) {
        (ans += dp[k][i]) %= mod;
      }
    }
    if (w == 1) {
      (ans += mod - 1) %= mod;
    }
  } else {
    ans = 1;
  }
  println(ans);
  return 0;
}