#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class t, class u>
void chmax(t& first, u second) {
  if (first < second) first = second;
}
template <class t, class u>
void chmin(t& first, u second) {
  if (second < first) first = second;
}
template <class t>
using vc = vector<t>;
template <class t>
using vvc = vc<vc<t>>;
using pi = pair<ll, ll>;
using vi = vc<ll>;
template <class t, class u>
ostream& operator<<(ostream& os, const pair<t, u>& p) {
  return os << "{" << p.first << "," << p.second << "}";
}
template <class t>
ostream& operator<<(ostream& os, const vc<t>& v) {
  os << "{";
  for (auto e : v) os << e << ",";
  return os << "}";
}
using uint = unsigned;
using ull = unsigned long long;
template <ll i, class T>
void print_tuple(ostream&, const T&) {}
template <ll i, class T, class H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ",";
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << "{";
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << "}";
}
void print(ll x, ll suc = 1) {
  cout << x;
  if (suc == 1) cout << "\n";
  if (suc == 2) cout << " ";
}
ll read() {
  ll i;
  cin >> i;
  return i;
}
vi readvi(ll n, ll off = 0) {
  vi v(n);
  for (ll i = ll(0); i < ll(n); i++) v[i] = read() + off;
  return v;
}
template <class T>
void print(const vector<T>& v, ll suc = 1) {
  for (ll i = ll(0); i < ll(v.size()); i++)
    print(v[i], i == ll(v.size()) - 1 ? suc : 2);
}
string readString() {
  string s;
  cin >> s;
  return s;
}
template <class T>
T sq(const T& t) {
  return t * t;
}
void yes(bool ex = true) {
  cout << "Yes" << endl;
  if (ex) exit(0);
}
void no(bool ex = true) {
  cout << "No" << endl;
  if (ex) exit(0);
}
constexpr ll ten(ll n) { return n == 0 ? 1 : ten(n - 1) * 10; }
const ll infLL = LLONG_MAX / 3;
const ll inf = infLL;
ll topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
ll topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
ll popcount(signed t) { return __builtin_popcount(t); }
ll popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(ll i) { return i && (i & -i) == i; }
bool inc(ll first, ll second, ll c) { return first <= second && second <= c; }
template <class t>
void mkuni(vc<t>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
ll rand_int(ll l, ll r) {
  static random_device rd;
  static mt19937_64 gen(rd());
  return uniform_int_distribution<ll>(l, r)(gen);
}
using uint = unsigned;
using ull = unsigned long long;
const uint mod = 1000000007;
struct mint {
  uint v;
  mint(ll vv = 0) { s(vv % mod + mod); }
  mint& s(uint vv) {
    v = vv < mod ? vv : vv - mod;
    return *this;
  }
  mint operator-() const { return mint() - *this; }
  mint& operator+=(const mint& rhs) { return s(v + rhs.v); }
  mint& operator-=(const mint& rhs) { return s(v + mod - rhs.v); }
  mint& operator*=(const mint& rhs) {
    v = ull(v) * rhs.v % mod;
    return *this;
  }
  mint& operator/=(const mint& rhs) { return *this *= rhs.inv(); }
  mint operator+(const mint& rhs) const { return mint(*this) += rhs; }
  mint operator-(const mint& rhs) const { return mint(*this) -= rhs; }
  mint operator*(const mint& rhs) const { return mint(*this) *= rhs; }
  mint operator/(const mint& rhs) const { return mint(*this) /= rhs; }
  mint pow(ll n) const {
    mint res(1), x(*this);
    while (n) {
      if (n & 1) res *= x;
      x *= x;
      n >>= 1;
    }
    return res;
  }
  mint inv() const { return pow(mod - 2); }
  friend ostream& operator<<(ostream& os, const mint& m) { return os << m.v; }
  bool operator<(const mint& r) const { return v < r.v; }
  bool operator==(const mint& r) const { return v == r.v; }
};
ll gcd(ll first, ll second) {
  return second ? gcd(second, first % second) : first;
}
struct unionfind {
  vi p, s;
  ll c;
  unionfind(ll n) : p(n, -1), s(n, 1), c(n) {}
  ll find(ll first) {
    return p[first] == -1 ? first : (p[first] = find(p[first]));
  }
  bool unite(ll first, ll second) {
    first = find(first);
    second = find(second);
    if (first == second) return false;
    p[second] = first;
    s[first] += s[second];
    c--;
    return true;
  }
  bool same(ll first, ll second) { return find(first) == find(second); }
  ll sz(ll first) { return s[find(first)]; }
};
ll cmpsA(ll n, ll x, ll y) {
  unionfind uf(n);
  for (ll i = ll(x); i < ll(n); i++) uf.unite(i - x, i);
  for (ll i = ll(y); i < ll(n); i++) uf.unite(i - y, i);
  return uf.c;
}
ll cmpsB(ll n, ll x, ll y) {
  ll w = x + y - gcd(x, y);
  if (w < n)
    return x + y - w;
  else
    return x + y - n;
}
const ll vmax = 100010;
bool pri[vmax];
ll w[vmax];
void initprime() {
  fill(pri + 2, pri + vmax, 1);
  fill(w + 1, w + vmax, 1);
  for (ll i = ll(2); i < ll(vmax); i++)
    if (pri[i]) {
      for (ll j = i * 2; j < vmax; j += i) pri[j] = 0;
      for (ll j = i; j < vmax; j += i) w[j] = -w[j];
      for (ll j = i * i; j < vmax; j += i * i) w[j] = 0;
    }
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
  initprime();
  ll n, k;
  cin >> n >> k;
  vc<mint> cnt(n + 1);
  for (ll g = ll(1); g < ll(n); g++) {
    ll m = (n - 1) / g;
    ll x = 0;
    for (ll i = 1; i <= m + 1; i++)
      if (w[i]) {
        ll t = (m + 1) / i;
        x += t * (t - 1) / 2 * w[i];
      }
    cnt[g] = x;
  }
  void(0);
  for (ll i = ll(0); i < ll(n - 1); i++) cnt[i] += n - 1 - i;
  void(0);
  for (ll g = ll(1); g < ll(n); g++) {
    ll m = (n - 1) / g;
    ll s = m + 1;
    for (ll x = ll(1); x < ll(s); x++)
      if (gcd(x, s - x) == 1) cnt[g * s - n] -= 1;
  }
  void(0);
  mint ans = 0;
  for (ll i = ll(1); i < ll(n + 1); i++) ans += cnt[i] * mint(k).pow(i);
  ans /= mint(k).pow(n);
  cout << ans << endl;
}

### Prompt

Develop a solution in CPP to the problem described below:

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>
using namespace std;
using ll = long long;
template <class t, class u>
void chmax(t& first, u second) {
  if (first < second) first = second;
}
template <class t, class u>
void chmin(t& first, u second) {
  if (second < first) first = second;
}
template <class t>
using vc = vector<t>;
template <class t>
using vvc = vc<vc<t>>;
using pi = pair<ll, ll>;
using vi = vc<ll>;
template <class t, class u>
ostream& operator<<(ostream& os, const pair<t, u>& p) {
  return os << "{" << p.first << "," << p.second << "}";
}
template <class t>
ostream& operator<<(ostream& os, const vc<t>& v) {
  os << "{";
  for (auto e : v) os << e << ",";
  return os << "}";
}
using uint = unsigned;
using ull = unsigned long long;
template <ll i, class T>
void print_tuple(ostream&, const T&) {}
template <ll i, class T, class H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ",";
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << "{";
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << "}";
}
void print(ll x, ll suc = 1) {
  cout << x;
  if (suc == 1) cout << "\n";
  if (suc == 2) cout << " ";
}
ll read() {
  ll i;
  cin >> i;
  return i;
}
vi readvi(ll n, ll off = 0) {
  vi v(n);
  for (ll i = ll(0); i < ll(n); i++) v[i] = read() + off;
  return v;
}
template <class T>
void print(const vector<T>& v, ll suc = 1) {
  for (ll i = ll(0); i < ll(v.size()); i++)
    print(v[i], i == ll(v.size()) - 1 ? suc : 2);
}
string readString() {
  string s;
  cin >> s;
  return s;
}
template <class T>
T sq(const T& t) {
  return t * t;
}
void yes(bool ex = true) {
  cout << "Yes" << endl;
  if (ex) exit(0);
}
void no(bool ex = true) {
  cout << "No" << endl;
  if (ex) exit(0);
}
constexpr ll ten(ll n) { return n == 0 ? 1 : ten(n - 1) * 10; }
const ll infLL = LLONG_MAX / 3;
const ll inf = infLL;
ll topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
ll topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
ll popcount(signed t) { return __builtin_popcount(t); }
ll popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(ll i) { return i && (i & -i) == i; }
bool inc(ll first, ll second, ll c) { return first <= second && second <= c; }
template <class t>
void mkuni(vc<t>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
ll rand_int(ll l, ll r) {
  static random_device rd;
  static mt19937_64 gen(rd());
  return uniform_int_distribution<ll>(l, r)(gen);
}
using uint = unsigned;
using ull = unsigned long long;
const uint mod = 1000000007;
struct mint {
  uint v;
  mint(ll vv = 0) { s(vv % mod + mod); }
  mint& s(uint vv) {
    v = vv < mod ? vv : vv - mod;
    return *this;
  }
  mint operator-() const { return mint() - *this; }
  mint& operator+=(const mint& rhs) { return s(v + rhs.v); }
  mint& operator-=(const mint& rhs) { return s(v + mod - rhs.v); }
  mint& operator*=(const mint& rhs) {
    v = ull(v) * rhs.v % mod;
    return *this;
  }
  mint& operator/=(const mint& rhs) { return *this *= rhs.inv(); }
  mint operator+(const mint& rhs) const { return mint(*this) += rhs; }
  mint operator-(const mint& rhs) const { return mint(*this) -= rhs; }
  mint operator*(const mint& rhs) const { return mint(*this) *= rhs; }
  mint operator/(const mint& rhs) const { return mint(*this) /= rhs; }
  mint pow(ll n) const {
    mint res(1), x(*this);
    while (n) {
      if (n & 1) res *= x;
      x *= x;
      n >>= 1;
    }
    return res;
  }
  mint inv() const { return pow(mod - 2); }
  friend ostream& operator<<(ostream& os, const mint& m) { return os << m.v; }
  bool operator<(const mint& r) const { return v < r.v; }
  bool operator==(const mint& r) const { return v == r.v; }
};
ll gcd(ll first, ll second) {
  return second ? gcd(second, first % second) : first;
}
struct unionfind {
  vi p, s;
  ll c;
  unionfind(ll n) : p(n, -1), s(n, 1), c(n) {}
  ll find(ll first) {
    return p[first] == -1 ? first : (p[first] = find(p[first]));
  }
  bool unite(ll first, ll second) {
    first = find(first);
    second = find(second);
    if (first == second) return false;
    p[second] = first;
    s[first] += s[second];
    c--;
    return true;
  }
  bool same(ll first, ll second) { return find(first) == find(second); }
  ll sz(ll first) { return s[find(first)]; }
};
ll cmpsA(ll n, ll x, ll y) {
  unionfind uf(n);
  for (ll i = ll(x); i < ll(n); i++) uf.unite(i - x, i);
  for (ll i = ll(y); i < ll(n); i++) uf.unite(i - y, i);
  return uf.c;
}
ll cmpsB(ll n, ll x, ll y) {
  ll w = x + y - gcd(x, y);
  if (w < n)
    return x + y - w;
  else
    return x + y - n;
}
const ll vmax = 100010;
bool pri[vmax];
ll w[vmax];
void initprime() {
  fill(pri + 2, pri + vmax, 1);
  fill(w + 1, w + vmax, 1);
  for (ll i = ll(2); i < ll(vmax); i++)
    if (pri[i]) {
      for (ll j = i * 2; j < vmax; j += i) pri[j] = 0;
      for (ll j = i; j < vmax; j += i) w[j] = -w[j];
      for (ll j = i * i; j < vmax; j += i * i) w[j] = 0;
    }
}
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
  initprime();
  ll n, k;
  cin >> n >> k;
  vc<mint> cnt(n + 1);
  for (ll g = ll(1); g < ll(n); g++) {
    ll m = (n - 1) / g;
    ll x = 0;
    for (ll i = 1; i <= m + 1; i++)
      if (w[i]) {
        ll t = (m + 1) / i;
        x += t * (t - 1) / 2 * w[i];
      }
    cnt[g] = x;
  }
  void(0);
  for (ll i = ll(0); i < ll(n - 1); i++) cnt[i] += n - 1 - i;
  void(0);
  for (ll g = ll(1); g < ll(n); g++) {
    ll m = (n - 1) / g;
    ll s = m + 1;
    for (ll x = ll(1); x < ll(s); x++)
      if (gcd(x, s - x) == 1) cnt[g * s - n] -= 1;
  }
  void(0);
  mint ans = 0;
  for (ll i = ll(1); i < ll(n + 1); i++) ans += cnt[i] * mint(k).pow(i);
  ans /= mint(k).pow(n);
  cout << ans << endl;
}

```