#include <bits/stdc++.h>
using namespace std;
void per() { cerr << endl; }
template <typename Head, typename... Tail>
void per(Head H, Tail... T) {
  cerr << H << ' ';
  per(T...);
}
template <class T>
bool uin(T& a, T b) {
  return a > b ? (a = b, true) : false;
}
template <class T>
bool uax(T& a, T b) {
  return a < b ? (a = b, true) : false;
}
template <class U, class V>
ostream& operator<<(ostream& out, const pair<U, V>& a) {
  return out << "(" << a.first << ", " << a.second << ")";
}
template <class U, class V>
istream& operator>>(istream& in, pair<U, V>& a) {
  return in >> a.first >> a.second;
}
template <typename W,
          typename T = typename enable_if<!is_same<W, string>::value,
                                          typename W::value_type>::type>
ostream& operator<<(ostream& out, const W& v) {
  out << "{ ";
  for (const auto& first : v) out << first << ", ";
  return out << '}';
}
template <class T>
void readArr(T from, T to) {
  for (auto i = from; i != to; ++i) cin >> *i;
}
mt19937 mrand(1337);
unsigned int myRand32() { return mrand() & (unsigned int)(-1); }
unsigned long long myRand64() {
  return ((unsigned long long)myRand32() << 32) ^ myRand32();
}
const int mod = 1000000007;
void add(int& a, int b) {
  a += b;
  if (a >= mod) a -= mod;
  if (a < 0) a += mod;
}
void dec(int& a, int b) {
  a -= b;
  if (a < 0) a += mod;
}
int mult(int a, int b) { return a * (long long)b % mod; }
int bp(int a, int b) {
  int res = 1;
  while (b > 0) {
    if (b & 1) res = mult(res, a);
    a = mult(a, a);
    b >>= 1;
  }
  return res;
}
int n, k;
vector<pair<int, int> > g[200007];
int a[200007];
const int MAXN = 2e5 + 7;
const size_t MAX_BIT = 18;
const size_t MAX_SIZE = 1 << MAX_BIT;
struct FenwickTree1 {
  int t[MAX_SIZE];
  int get(int v) {
    int res = 0;
    for (; v >= 0; v = (v & (v + 1)) - 1) {
      add(res, t[v]);
    }
    return res;
  }
  int get(int vl, int vr) {
    if (vl > vr) return 0;
    int res = get(vr);
    if (vl > 0) {
      dec(res, get(vl - 1));
    }
    return res;
  }
  void up(int v, int val) {
    for (; v < MAX_SIZE; v = v | (v + 1)) {
      add(t[v], val);
    }
  }
} F[2], G[2];
int RES = 0;
class CentroidDecomposition {
 public:
  int n;
  int w[MAXN];
  int del[MAXN];
  void CalcW(int v, int p = -1) {
    w[v] = 1;
    for (auto [to, _] : g[v])
      if (to != p && !del[to]) {
        CalcW(to, v);
        w[v] += w[to];
      }
  }
  int FindCentroid(int v, int total_w, int p = -1) {
    for (auto [to, _] : g[v])
      if (to != p && !del[to] && 2 * w[to] > total_w) {
        return FindCentroid(to, total_w, v);
      }
    return v;
  }
  void col(int v, int p, int first, int last, int co, int zn, int sum) {
    add(sum, a[v]);
    F[first].up(co, zn * sum);
    G[first].up(co, zn);
    for (auto [to, be] : g[v])
      if (to != p && !del[to]) {
        col(to, v, first, be, co + (be != last), zn, sum);
      }
  }
  void go(int v, int p, int first, int last, int co, int sum) {
    if (co > k) return;
    add(sum, a[v]);
    add(RES, F[first].get(0, k - co));
    add(RES, F[first ^ 1].get(0, k - co - 1));
    add(RES, mult(sum, G[first].get(0, k - co)));
    add(RES, mult(sum, G[first ^ 1].get(0, k - co - 1)));
    for (auto [to, be] : g[v])
      if (to != p && !del[to]) {
        go(to, v, first, be, co + (be != last), sum);
      }
  }
  int Build(int v) {
    CalcW(v);
    int c = FindCentroid(v, w[v]);
    for (auto [to, be] : g[c])
      if (!del[to]) {
        col(to, c, be, be, 0, 1, 0);
      }
    add(RES, a[c]);
    add(RES, F[0].get(0, k));
    add(RES, F[1].get(0, k));
    add(RES, mult(a[c], G[0].get(0, k)));
    add(RES, mult(a[c], G[1].get(0, k)));
    for (auto [to, be] : g[c])
      if (!del[to]) {
        col(to, c, be, be, 0, -1, 0);
        go(to, c, be, be, 0, a[c]);
      }
    del[c] = 1;
    for (auto [to, _] : g[c])
      if (!del[to]) {
        Build(to);
      }
    return c;
  }
} KEK;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> k;
  readArr(a, a + n);
  for (int i = 0; i < n - 1; ++i) {
    int w1, w2, w3;
    cin >> w1 >> w2 >> w3;
    --w1;
    --w2;
    g[w1].push_back(make_pair(w2, w3));
    g[w2].push_back(make_pair(w1, w3));
  }
  KEK.Build(0);
  cout << RES;
}

### Prompt

In Cpp, your task is to solve the following problem:

There is a city park represented as a tree with n attractions as its vertices and n - 1 rails as its edges. The i-th attraction has happiness value a_i.

Each rail has a color. It is either black if t_i = 0, or white if t_i = 1. Black trains only operate on a black rail track, and white trains only operate on a white rail track. If you are previously on a black train and want to ride a white train, or you are previously on a white train and want to ride a black train, you need to use 1 ticket.

The path of a tour must be a simple path — it must not visit an attraction more than once. You do not need a ticket the first time you board a train. You only have k tickets, meaning you can only switch train types at most k times. In particular, you do not need a ticket to go through a path consisting of one rail color.

Define f(u, v) as the sum of happiness values of the attractions in the tour (u, v), which is a simple path that starts at the u-th attraction and ends at the v-th attraction. Find the sum of f(u,v) for all valid tours (u, v) (1 ≤ u ≤ v ≤ n) that does not need more than k tickets, modulo 10^9 + 7.

Input

The first line contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5, 0 ≤ k ≤ n-1) — the number of attractions in the city park and the number of tickets you have.

The second line contains n integers a_1, a_2,…, a_n (0 ≤ a_i ≤ 10^9) — the happiness value of each attraction.

The i-th of the next n - 1 lines contains three integers u_i, v_i, and t_i (1 ≤ u_i, v_i ≤ n, 0 ≤ t_i ≤ 1) — an edge between vertices u_i and v_i with color t_i. The given edges form a tree.

Output

Output an integer denoting the total happiness value for all valid tours (u, v) (1 ≤ u ≤ v ≤ n), modulo 10^9 + 7.

Examples

Input


5 0
1 3 2 6 4
1 2 1
1 4 0
3 2 1
2 5 0


Output


45


Input


3 1
1 1 1
1 2 1
3 2 0


Output


10

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
void per() { cerr << endl; }
template <typename Head, typename... Tail>
void per(Head H, Tail... T) {
  cerr << H << ' ';
  per(T...);
}
template <class T>
bool uin(T& a, T b) {
  return a > b ? (a = b, true) : false;
}
template <class T>
bool uax(T& a, T b) {
  return a < b ? (a = b, true) : false;
}
template <class U, class V>
ostream& operator<<(ostream& out, const pair<U, V>& a) {
  return out << "(" << a.first << ", " << a.second << ")";
}
template <class U, class V>
istream& operator>>(istream& in, pair<U, V>& a) {
  return in >> a.first >> a.second;
}
template <typename W,
          typename T = typename enable_if<!is_same<W, string>::value,
                                          typename W::value_type>::type>
ostream& operator<<(ostream& out, const W& v) {
  out << "{ ";
  for (const auto& first : v) out << first << ", ";
  return out << '}';
}
template <class T>
void readArr(T from, T to) {
  for (auto i = from; i != to; ++i) cin >> *i;
}
mt19937 mrand(1337);
unsigned int myRand32() { return mrand() & (unsigned int)(-1); }
unsigned long long myRand64() {
  return ((unsigned long long)myRand32() << 32) ^ myRand32();
}
const int mod = 1000000007;
void add(int& a, int b) {
  a += b;
  if (a >= mod) a -= mod;
  if (a < 0) a += mod;
}
void dec(int& a, int b) {
  a -= b;
  if (a < 0) a += mod;
}
int mult(int a, int b) { return a * (long long)b % mod; }
int bp(int a, int b) {
  int res = 1;
  while (b > 0) {
    if (b & 1) res = mult(res, a);
    a = mult(a, a);
    b >>= 1;
  }
  return res;
}
int n, k;
vector<pair<int, int> > g[200007];
int a[200007];
const int MAXN = 2e5 + 7;
const size_t MAX_BIT = 18;
const size_t MAX_SIZE = 1 << MAX_BIT;
struct FenwickTree1 {
  int t[MAX_SIZE];
  int get(int v) {
    int res = 0;
    for (; v >= 0; v = (v & (v + 1)) - 1) {
      add(res, t[v]);
    }
    return res;
  }
  int get(int vl, int vr) {
    if (vl > vr) return 0;
    int res = get(vr);
    if (vl > 0) {
      dec(res, get(vl - 1));
    }
    return res;
  }
  void up(int v, int val) {
    for (; v < MAX_SIZE; v = v | (v + 1)) {
      add(t[v], val);
    }
  }
} F[2], G[2];
int RES = 0;
class CentroidDecomposition {
 public:
  int n;
  int w[MAXN];
  int del[MAXN];
  void CalcW(int v, int p = -1) {
    w[v] = 1;
    for (auto [to, _] : g[v])
      if (to != p && !del[to]) {
        CalcW(to, v);
        w[v] += w[to];
      }
  }
  int FindCentroid(int v, int total_w, int p = -1) {
    for (auto [to, _] : g[v])
      if (to != p && !del[to] && 2 * w[to] > total_w) {
        return FindCentroid(to, total_w, v);
      }
    return v;
  }
  void col(int v, int p, int first, int last, int co, int zn, int sum) {
    add(sum, a[v]);
    F[first].up(co, zn * sum);
    G[first].up(co, zn);
    for (auto [to, be] : g[v])
      if (to != p && !del[to]) {
        col(to, v, first, be, co + (be != last), zn, sum);
      }
  }
  void go(int v, int p, int first, int last, int co, int sum) {
    if (co > k) return;
    add(sum, a[v]);
    add(RES, F[first].get(0, k - co));
    add(RES, F[first ^ 1].get(0, k - co - 1));
    add(RES, mult(sum, G[first].get(0, k - co)));
    add(RES, mult(sum, G[first ^ 1].get(0, k - co - 1)));
    for (auto [to, be] : g[v])
      if (to != p && !del[to]) {
        go(to, v, first, be, co + (be != last), sum);
      }
  }
  int Build(int v) {
    CalcW(v);
    int c = FindCentroid(v, w[v]);
    for (auto [to, be] : g[c])
      if (!del[to]) {
        col(to, c, be, be, 0, 1, 0);
      }
    add(RES, a[c]);
    add(RES, F[0].get(0, k));
    add(RES, F[1].get(0, k));
    add(RES, mult(a[c], G[0].get(0, k)));
    add(RES, mult(a[c], G[1].get(0, k)));
    for (auto [to, be] : g[c])
      if (!del[to]) {
        col(to, c, be, be, 0, -1, 0);
        go(to, c, be, be, 0, a[c]);
      }
    del[c] = 1;
    for (auto [to, _] : g[c])
      if (!del[to]) {
        Build(to);
      }
    return c;
  }
} KEK;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> k;
  readArr(a, a + n);
  for (int i = 0; i < n - 1; ++i) {
    int w1, w2, w3;
    cin >> w1 >> w2 >> w3;
    --w1;
    --w2;
    g[w1].push_back(make_pair(w2, w3));
    g[w2].push_back(make_pair(w1, w3));
  }
  KEK.Build(0);
  cout << RES;
}

```