#include <bits/stdc++.h>
template <typename Tp>
inline void read(Tp& x) {
  x = 0;
  bool fg = 0;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') fg ^= 1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9')
    x = (x << 1) + (x << 3) + (Tp)(ch ^ 48), ch = getchar();
  if (fg) x = -x;
}
template <typename Tp, typename... Args>
void read(Tp& t, Args&... args) {
  read(t);
  read(args...);
}
using namespace std;
const int N = 100010;
const int mod = 1e9 + 7;
int n, k;
int p[N], phi[N], tot;
bool v[N];
void init(int n) {
  for (int i = 2; i <= n; ++i) {
    if (!v[i]) p[++tot] = i, phi[i] = i - 1;
    for (int j = 1; j <= tot && p[j] * i <= n; ++j) {
      v[i * p[j]] = 1;
      if (i % p[j] == 0) {
        phi[i * p[j]] = phi[i] * p[j];
        break;
      }
      phi[i * p[j]] = phi[i] * (p[j] - 1);
    }
  }
  phi[1] = 1;
}
long long qpow(long long a, long long b = mod - 2) {
  if (b < 0) return qpow(qpow(a, -b));
  long long r = 1;
  for (; b; b >>= 1, a = a * a % mod)
    if (b & 1) r = r * a % mod;
  return r;
}
int gcd(int a, int b) { return !b ? a : gcd(b, a % b); }
template <typename Tp>
void Add(Tp& x, Tp y) {
  x = (x + y) % mod;
}
template <typename Tp>
void Sub(Tp& x, Tp y) {
  x = ((x - y) % mod + mod) % mod;
}
template <typename Tp>
void Mul(Tp& x, Tp y) {
  x = x * y % mod;
}
void baoli() {
  long long ans = 0;
  for (int i = 1; i < n; ++i) {
    for (int j = 1; j < n; ++j) {
      Add(ans, qpow(k, max(i + j - n, gcd(i, j))));
    }
  }
  Mul(ans, qpow(qpow(k, n)));
  cout << ans << endl;
}
int main() {
  cin >> n >> k;
  init(n);
  long long ans = 0, pw = k;
  for (int s = 2; s <= 2 * n - 2; ++s) {
    Mul(pw, (long long)k);
    int cnt = (s <= n) ? (s - 1) : (2 * n - 1 - s);
    Add(ans, pw * cnt % mod);
  }
  Mul(ans, qpow(qpow(k, n)));
  long long tp1 = 0, tp2 = 0;
  pw = 1;
  for (int d = 1; d < n; ++d) {
    Mul(pw, (long long)k);
    long long tmp = 0;
    for (int s = 2; d * s - d < n; ++s) Add(tmp, (long long)phi[s]);
    Add(tp1, pw * tmp % mod);
  }
  for (int d = 1; d < n; ++d) {
    long long tmp = 0, dt = qpow(k, d);
    pw = dt;
    for (int s = 2; d * s - d < n; ++s) {
      Mul(pw, dt);
      Add(tmp, pw * phi[s] % mod);
    }
    Add(tp2, tmp);
  }
  Mul(tp2, qpow(qpow(k, n)));
  ans = (ans + tp1 - tp2 + mod) % mod;
  Mul(ans, qpow(qpow(k, n)));
  cout << ans << endl;
  return 0;
}

### Prompt

Please create a solution in Cpp to the following problem:

You are given integers n, k. Let's consider the alphabet consisting of k different elements.

Let beauty f(s) of the string s be the number of indexes i, 1≤ i<|s|, for which prefix of s of length i equals to suffix of s of length i. For example, beauty of the string abacaba equals 2, as for i = 1, 3 prefix and suffix of length i are equal.

Consider all words of length n in the given alphabet. Find the expected value of f(s)^2 of a uniformly chosen at random word. We can show that it can be expressed as P/Q, where P and Q are coprime and Q isn't divided by 10^9 + 7. Output P⋅ Q^{-1} mod 10^9 + 7.

Input

The first and the only line contains two integers n, k (1≤ n ≤ 10^5, 1≤ k≤ 10^9) — the length of a string and the size of alphabet respectively.

Output

Output a single integer — P× Q^{-1} mod 10^9 + 7.

Examples

Input


2 3


Output


333333336


Input


1 5


Output


0


Input


100 1


Output


9801


Input


10 10


Output


412377396

Note

In the first example, there are 9 words of length 2 in alphabet of size 3 — aa, ab, ac, ba, bb, bc, ca, cb, cc. 3 of them have beauty 1 and 6 of them have beauty 0, so the average value is 1/3.

In the third example, there is only one such word, and it has beauty 99, so the average value is 99^2.

### Response

```cpp
#include <bits/stdc++.h>
template <typename Tp>
inline void read(Tp& x) {
  x = 0;
  bool fg = 0;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') fg ^= 1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9')
    x = (x << 1) + (x << 3) + (Tp)(ch ^ 48), ch = getchar();
  if (fg) x = -x;
}
template <typename Tp, typename... Args>
void read(Tp& t, Args&... args) {
  read(t);
  read(args...);
}
using namespace std;
const int N = 100010;
const int mod = 1e9 + 7;
int n, k;
int p[N], phi[N], tot;
bool v[N];
void init(int n) {
  for (int i = 2; i <= n; ++i) {
    if (!v[i]) p[++tot] = i, phi[i] = i - 1;
    for (int j = 1; j <= tot && p[j] * i <= n; ++j) {
      v[i * p[j]] = 1;
      if (i % p[j] == 0) {
        phi[i * p[j]] = phi[i] * p[j];
        break;
      }
      phi[i * p[j]] = phi[i] * (p[j] - 1);
    }
  }
  phi[1] = 1;
}
long long qpow(long long a, long long b = mod - 2) {
  if (b < 0) return qpow(qpow(a, -b));
  long long r = 1;
  for (; b; b >>= 1, a = a * a % mod)
    if (b & 1) r = r * a % mod;
  return r;
}
int gcd(int a, int b) { return !b ? a : gcd(b, a % b); }
template <typename Tp>
void Add(Tp& x, Tp y) {
  x = (x + y) % mod;
}
template <typename Tp>
void Sub(Tp& x, Tp y) {
  x = ((x - y) % mod + mod) % mod;
}
template <typename Tp>
void Mul(Tp& x, Tp y) {
  x = x * y % mod;
}
void baoli() {
  long long ans = 0;
  for (int i = 1; i < n; ++i) {
    for (int j = 1; j < n; ++j) {
      Add(ans, qpow(k, max(i + j - n, gcd(i, j))));
    }
  }
  Mul(ans, qpow(qpow(k, n)));
  cout << ans << endl;
}
int main() {
  cin >> n >> k;
  init(n);
  long long ans = 0, pw = k;
  for (int s = 2; s <= 2 * n - 2; ++s) {
    Mul(pw, (long long)k);
    int cnt = (s <= n) ? (s - 1) : (2 * n - 1 - s);
    Add(ans, pw * cnt % mod);
  }
  Mul(ans, qpow(qpow(k, n)));
  long long tp1 = 0, tp2 = 0;
  pw = 1;
  for (int d = 1; d < n; ++d) {
    Mul(pw, (long long)k);
    long long tmp = 0;
    for (int s = 2; d * s - d < n; ++s) Add(tmp, (long long)phi[s]);
    Add(tp1, pw * tmp % mod);
  }
  for (int d = 1; d < n; ++d) {
    long long tmp = 0, dt = qpow(k, d);
    pw = dt;
    for (int s = 2; d * s - d < n; ++s) {
      Mul(pw, dt);
      Add(tmp, pw * phi[s] % mod);
    }
    Add(tp2, tmp);
  }
  Mul(tp2, qpow(qpow(k, n)));
  ans = (ans + tp1 - tp2 + mod) % mod;
  Mul(ans, qpow(qpow(k, n)));
  cout << ans << endl;
  return 0;
}

```