#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 10, mod = 1e9 + 7;
namespace fft {
struct num {
  double x, y;
  num() { x = y = 0; }
  num(double x, double y) : x(x), y(y) {}
};
inline num operator+(num a, num b) { return num(a.x + b.x, a.y + b.y); }
inline num operator-(num a, num b) { return num(a.x - b.x, a.y - b.y); }
inline num operator*(num a, num b) {
  return num(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);
}
inline num conj(num a) { return num(a.x, -a.y); }
int base = 1;
vector<num> roots = {{0, 0}, {1, 0}};
vector<int> rev = {0, 1};
const double PI = acosl(-1.0);
void ensure_base(int nbase) {
  if (nbase <= base) return;
  rev.resize(1 << nbase);
  for (int i = 0; i < (1 << nbase); i++)
    rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
  roots.resize(1 << nbase);
  while (base < nbase) {
    double angle = 2 * PI / (1 << (base + 1));
    for (int i = 1 << (base - 1); i < (1 << base); i++) {
      roots[i << 1] = roots[i];
      double angle_i = angle * (2 * i + 1 - (1 << base));
      roots[(i << 1) + 1] = num(cos(angle_i), sin(angle_i));
    }
    base++;
  }
}
void fft(vector<num> &a, int n = -1) {
  if (n == -1) n = a.size();
  assert((n & (n - 1)) == 0);
  int zeros = __builtin_ctz(n);
  ensure_base(zeros);
  int shift = base - zeros;
  for (int i = 0; i < n; i++)
    if (i < (rev[i] >> shift)) swap(a[i], a[rev[i] >> shift]);
  for (int k = 1; k < n; k <<= 1) {
    for (int i = 0; i < n; i += 2 * k) {
      for (int j = 0; j < k; j++) {
        num z = a[i + j + k] * roots[j + k];
        a[i + j + k] = a[i + j] - z;
        a[i + j] = a[i + j] + z;
      }
    }
  }
}
vector<num> fa, fb;
vector<int> multiply(vector<int> &a, vector<int> &b) {
  int need = a.size() + b.size() - 1;
  int nbase = 0;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if (sz > (int)fa.size()) fa.resize(sz);
  for (int i = 0; i < sz; i++) {
    int x = (i < (int)a.size() ? a[i] : 0);
    int y = (i < (int)b.size() ? b[i] : 0);
    fa[i] = num(x, y);
  }
  fft(fa, sz);
  num r(0, -0.25 / sz);
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    num z = (fa[j] * fa[j] - conj(fa[i] * fa[i])) * r;
    if (i != j) fa[j] = (fa[i] * fa[i] - conj(fa[j] * fa[j])) * r;
    fa[i] = z;
  }
  fft(fa, sz);
  vector<int> res(need);
  for (int i = 0; i < need; i++) res[i] = fa[i].x + 0.5;
  return res;
}
vector<int> multiply_mod(vector<int> &a, vector<int> &b, int m, int eq = 0) {
  int need = a.size() + b.size() - 1;
  int nbase = 0;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if (sz > (int)fa.size()) fa.resize(sz);
  for (int i = 0; i < (int)a.size(); i++) {
    int x = (a[i] % m + m) % m;
    fa[i] = num(x & ((1 << 15) - 1), x >> 15);
  }
  fill(fa.begin() + a.size(), fa.begin() + sz, num{0, 0});
  fft(fa, sz);
  if (sz > (int)fb.size()) fb.resize(sz);
  if (eq)
    copy(fa.begin(), fa.begin() + sz, fb.begin());
  else {
    for (int i = 0; i < (int)b.size(); i++) {
      int x = (b[i] % m + m) % m;
      fb[i] = num(x & ((1 << 15) - 1), x >> 15);
    }
    fill(fb.begin() + b.size(), fb.begin() + sz, num{0, 0});
    fft(fb, sz);
  }
  double ratio = 0.25 / sz;
  num r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    num a1 = (fa[i] + conj(fa[j]));
    num a2 = (fa[i] - conj(fa[j])) * r2;
    num b1 = (fb[i] + conj(fb[j])) * r3;
    num b2 = (fb[i] - conj(fb[j])) * r4;
    if (i != j) {
      num c1 = (fa[j] + conj(fa[i]));
      num c2 = (fa[j] - conj(fa[i])) * r2;
      num d1 = (fb[j] + conj(fb[i])) * r3;
      num d2 = (fb[j] - conj(fb[i])) * r4;
      fa[i] = c1 * d1 + c2 * d2 * r5;
      fb[i] = c1 * d2 + c2 * d1;
    }
    fa[j] = a1 * b1 + a2 * b2 * r5;
    fb[j] = a1 * b2 + a2 * b1;
  }
  fft(fa, sz);
  fft(fb, sz);
  vector<int> res(need);
  for (int i = 0; i < need; i++) {
    long long aa = fa[i].x + 0.5;
    long long bb = fb[i].x + 0.5;
    long long cc = fa[i].y + 0.5;
    res[i] = (aa + ((bb % m) << 15) + ((cc % m) << 30)) % m;
  }
  return res;
}
vector<int> square_mod(vector<int> &a, int m) {
  return multiply_mod(a, a, m, 1);
}
};  // namespace fft
long long F[1000000];
long long iF[1000000];
long long P(long long a, long long b) {
  if (b == 0) return 1;
  long long x = P(a, b / 2);
  x = (x * x) % mod;
  if (b % 2) x = (x * a) % mod;
  return x;
}
long long inv(long long x) { return P(x, mod - 2); }
vector<int> one;
void prepare(vector<int> &v, int len) {
  for (int i = 0; i < v.size(); i++) {
    long long cur = v[i];
    cur = cur * P(2, len * 1LL * i);
    cur %= mod;
    v[i] = cur;
  }
}
int k;
long long C(long long A, long long B) {
  return (((F[A] * iF[B]) % mod) * iF[A - B]) % mod;
}
vector<int> solve(int n) {
  if (n == 1) return one;
  int len = n / 2;
  vector<int> L, R;
  if (n % 2) {
    L = solve(n - 1);
    R = one;
    len = 1;
  } else {
    L = solve(n / 2);
    R = L;
  }
  prepare(L, len);
  vector<int> ret = fft::multiply_mod(L, R, mod);
  while (ret.size() > k + 1) ret.pop_back();
  return ret;
}
int main() {
  long long n;
  cin >> n >> k;
  F[0] = 1;
  iF[0] = 1;
  for (int i = 1; i <= k; i++) {
    F[i] = (F[i - 1] * i) % mod;
    iF[i] = inv(F[i]);
  }
  if (n > k) {
    puts("0");
    return 0;
  }
  for (int i = 0; i <= k; i++) one.push_back((iF[i]) % mod);
  one[0] = 0;
  vector<int> ret = solve(n);
  long long ans = 0;
  for (int i = 0; i <= k; i++) {
    ans += (((ret[i] * 1LL * F[i]) % mod) * C(k, i)) % mod;
    ans %= mod;
  }
  cout << ans << endl;
}

### Prompt

Generate a cpp solution to the following problem:

Let's define the transformation P of a sequence of integers a1, a2, ..., an as b1, b2, ..., bn, where bi = a1 | a2 | ... | ai for all i = 1, 2, ..., n, where | is the bitwise OR operation.

Vasya consequently applies the transformation P to all sequences of length n consisting of integers from 1 to 2k - 1 inclusive. He wants to know how many of these sequences have such property that their transformation is a strictly increasing sequence. Help him to calculate this number modulo 109 + 7.

Input

The only line of the input contains two integers n and k (1 ≤ n ≤ 1018, 1 ≤ k ≤ 30 000).

Output

Print a single integer — the answer to the problem modulo 109 + 7.

Examples

Input

1 2


Output

3


Input

2 3


Output

30


Input

3 3


Output

48

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int N = 1e5 + 10, mod = 1e9 + 7;
namespace fft {
struct num {
  double x, y;
  num() { x = y = 0; }
  num(double x, double y) : x(x), y(y) {}
};
inline num operator+(num a, num b) { return num(a.x + b.x, a.y + b.y); }
inline num operator-(num a, num b) { return num(a.x - b.x, a.y - b.y); }
inline num operator*(num a, num b) {
  return num(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);
}
inline num conj(num a) { return num(a.x, -a.y); }
int base = 1;
vector<num> roots = {{0, 0}, {1, 0}};
vector<int> rev = {0, 1};
const double PI = acosl(-1.0);
void ensure_base(int nbase) {
  if (nbase <= base) return;
  rev.resize(1 << nbase);
  for (int i = 0; i < (1 << nbase); i++)
    rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
  roots.resize(1 << nbase);
  while (base < nbase) {
    double angle = 2 * PI / (1 << (base + 1));
    for (int i = 1 << (base - 1); i < (1 << base); i++) {
      roots[i << 1] = roots[i];
      double angle_i = angle * (2 * i + 1 - (1 << base));
      roots[(i << 1) + 1] = num(cos(angle_i), sin(angle_i));
    }
    base++;
  }
}
void fft(vector<num> &a, int n = -1) {
  if (n == -1) n = a.size();
  assert((n & (n - 1)) == 0);
  int zeros = __builtin_ctz(n);
  ensure_base(zeros);
  int shift = base - zeros;
  for (int i = 0; i < n; i++)
    if (i < (rev[i] >> shift)) swap(a[i], a[rev[i] >> shift]);
  for (int k = 1; k < n; k <<= 1) {
    for (int i = 0; i < n; i += 2 * k) {
      for (int j = 0; j < k; j++) {
        num z = a[i + j + k] * roots[j + k];
        a[i + j + k] = a[i + j] - z;
        a[i + j] = a[i + j] + z;
      }
    }
  }
}
vector<num> fa, fb;
vector<int> multiply(vector<int> &a, vector<int> &b) {
  int need = a.size() + b.size() - 1;
  int nbase = 0;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if (sz > (int)fa.size()) fa.resize(sz);
  for (int i = 0; i < sz; i++) {
    int x = (i < (int)a.size() ? a[i] : 0);
    int y = (i < (int)b.size() ? b[i] : 0);
    fa[i] = num(x, y);
  }
  fft(fa, sz);
  num r(0, -0.25 / sz);
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    num z = (fa[j] * fa[j] - conj(fa[i] * fa[i])) * r;
    if (i != j) fa[j] = (fa[i] * fa[i] - conj(fa[j] * fa[j])) * r;
    fa[i] = z;
  }
  fft(fa, sz);
  vector<int> res(need);
  for (int i = 0; i < need; i++) res[i] = fa[i].x + 0.5;
  return res;
}
vector<int> multiply_mod(vector<int> &a, vector<int> &b, int m, int eq = 0) {
  int need = a.size() + b.size() - 1;
  int nbase = 0;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if (sz > (int)fa.size()) fa.resize(sz);
  for (int i = 0; i < (int)a.size(); i++) {
    int x = (a[i] % m + m) % m;
    fa[i] = num(x & ((1 << 15) - 1), x >> 15);
  }
  fill(fa.begin() + a.size(), fa.begin() + sz, num{0, 0});
  fft(fa, sz);
  if (sz > (int)fb.size()) fb.resize(sz);
  if (eq)
    copy(fa.begin(), fa.begin() + sz, fb.begin());
  else {
    for (int i = 0; i < (int)b.size(); i++) {
      int x = (b[i] % m + m) % m;
      fb[i] = num(x & ((1 << 15) - 1), x >> 15);
    }
    fill(fb.begin() + b.size(), fb.begin() + sz, num{0, 0});
    fft(fb, sz);
  }
  double ratio = 0.25 / sz;
  num r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    num a1 = (fa[i] + conj(fa[j]));
    num a2 = (fa[i] - conj(fa[j])) * r2;
    num b1 = (fb[i] + conj(fb[j])) * r3;
    num b2 = (fb[i] - conj(fb[j])) * r4;
    if (i != j) {
      num c1 = (fa[j] + conj(fa[i]));
      num c2 = (fa[j] - conj(fa[i])) * r2;
      num d1 = (fb[j] + conj(fb[i])) * r3;
      num d2 = (fb[j] - conj(fb[i])) * r4;
      fa[i] = c1 * d1 + c2 * d2 * r5;
      fb[i] = c1 * d2 + c2 * d1;
    }
    fa[j] = a1 * b1 + a2 * b2 * r5;
    fb[j] = a1 * b2 + a2 * b1;
  }
  fft(fa, sz);
  fft(fb, sz);
  vector<int> res(need);
  for (int i = 0; i < need; i++) {
    long long aa = fa[i].x + 0.5;
    long long bb = fb[i].x + 0.5;
    long long cc = fa[i].y + 0.5;
    res[i] = (aa + ((bb % m) << 15) + ((cc % m) << 30)) % m;
  }
  return res;
}
vector<int> square_mod(vector<int> &a, int m) {
  return multiply_mod(a, a, m, 1);
}
};  // namespace fft
long long F[1000000];
long long iF[1000000];
long long P(long long a, long long b) {
  if (b == 0) return 1;
  long long x = P(a, b / 2);
  x = (x * x) % mod;
  if (b % 2) x = (x * a) % mod;
  return x;
}
long long inv(long long x) { return P(x, mod - 2); }
vector<int> one;
void prepare(vector<int> &v, int len) {
  for (int i = 0; i < v.size(); i++) {
    long long cur = v[i];
    cur = cur * P(2, len * 1LL * i);
    cur %= mod;
    v[i] = cur;
  }
}
int k;
long long C(long long A, long long B) {
  return (((F[A] * iF[B]) % mod) * iF[A - B]) % mod;
}
vector<int> solve(int n) {
  if (n == 1) return one;
  int len = n / 2;
  vector<int> L, R;
  if (n % 2) {
    L = solve(n - 1);
    R = one;
    len = 1;
  } else {
    L = solve(n / 2);
    R = L;
  }
  prepare(L, len);
  vector<int> ret = fft::multiply_mod(L, R, mod);
  while (ret.size() > k + 1) ret.pop_back();
  return ret;
}
int main() {
  long long n;
  cin >> n >> k;
  F[0] = 1;
  iF[0] = 1;
  for (int i = 1; i <= k; i++) {
    F[i] = (F[i - 1] * i) % mod;
    iF[i] = inv(F[i]);
  }
  if (n > k) {
    puts("0");
    return 0;
  }
  for (int i = 0; i <= k; i++) one.push_back((iF[i]) % mod);
  one[0] = 0;
  vector<int> ret = solve(n);
  long long ans = 0;
  for (int i = 0; i <= k; i++) {
    ans += (((ret[i] * 1LL * F[i]) % mod) * C(k, i)) % mod;
    ans %= mod;
  }
  cout << ans << endl;
}

```