You are given a tree (a connected undirected graph without cycles) of n vertices. Each of the n - 1 edges of the tree is colored in either black or red.

You are also given an integer k. Consider sequences of k vertices. Let's call a sequence [a_1, a_2, …, a_k] good if it satisfies the following criterion:

  * We will walk a path (possibly visiting same edge/vertex multiple times) on the tree, starting from a_1 and ending at a_k. 
  * Start at a_1, then go to a_2 using the shortest path between a_1 and a_2, then go to a_3 in a similar way, and so on, until you travel the shortest path between a_{k-1} and a_k.
  * If you walked over at least one black edge during this process, then the sequence is good. 

<image>

Consider the tree on the picture. If k=3 then the following sequences are good: [1, 4, 7], [5, 5, 3] and [2, 3, 7]. The following sequences are not good: [1, 4, 6], [5, 5, 5], [3, 7, 3].

There are n^k sequences of vertices, count how many of them are good. Since this number can be quite large, print it modulo 10^9+7.

Input

The first line contains two integers n and k (2 ≤ n ≤ 10^5, 2 ≤ k ≤ 100), the size of the tree and the length of the vertex sequence.

Each of the next n - 1 lines contains three integers u_i, v_i and x_i (1 ≤ u_i, v_i ≤ n, x_i ∈ \{0, 1\}), where u_i and v_i denote the endpoints of the corresponding edge and x_i is the color of this edge (0 denotes red edge and 1 denotes black edge).

Output

Print the number of good sequences modulo 10^9 + 7.

Examples

Input


4 4
1 2 1
2 3 1
3 4 1


Output


252

Input


4 6
1 2 0
1 3 0
1 4 0


Output


0

Input


3 5
1 2 1
2 3 0


Output


210

Note

In the first example, all sequences (4^4) of length 4 except the following are good: 

  * [1, 1, 1, 1]
  * [2, 2, 2, 2]
  * [3, 3, 3, 3]
  * [4, 4, 4, 4] 



In the second example, all edges are red, hence there aren't any good sequences.
// #pragma GCC optimize("Ofast")
// #pragma GCC target("avx,avx2,fma")
// #pragma GCC optimization ("unroll-loops")

#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;

#define fo(i,n)         for(int i=0;i<n;i++)
#define nl              "\n"
#define ff              first
#define ss              second
#define int             long long
#define pb              push_back
#define mp              make_pair
#define vec(x)          vector<x>
#define matrix(x)       vector<vector<x>>
#define sz(x)           (int)x.size()
#define mem(a,b)        memset(a, b, sizeof a)
#define vii             vector<pair<int,int>>
#define pii             pair<int,int>
#define vi              vector<int>
#define mii             map<int,int>
#define uii             unordered_map<int,int,custom_hash>
#define pqb             priority_queue<int>
#define pqs             priority_queue<int,vi,greater<int> >
#define gcd(a,b)        __gcd(a,b)
#define lcm(a,b)        (a*(b/gcd(a,b)))
#define setbits(x)      __builtin_popcountll(x)
#define zrobits(x)      __builtin_ctzll(x)
#define mod             1000000007
#define MOD             998244353
#define inf             1e18
#define ps(x,y)         fixed<<setprecision(y)<<x
#define mk(arr,n,type)  type *arr=new type[n];
#define w(x)            int x; cin>>x; while(x--)
#define all(v)          v.begin(),v.end()
#define rep(i,a,b)      for (int i = a; i<b; ++i)
#define len(s)          s.length()

#define deb(x)          cerr <<#x<<" = "<<x<<"\n"
#define watch(x)        cout << #x << " = " << x << endl

mt19937                 rng(chrono::steady_clock::now().time_since_epoch().count());

typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> pbds; //for storing unique elements
typedef tree<int , null_type , less_equal<int> , rb_tree_tag , tree_order_statistics_node_update> ordered_set; //for repeating elements
 
int power(int a,int b,int m=mod)
{int ans=1;while(b>0){if(b&1)ans=(ans*a)%m;a=(a*a)%m;b>>=1;}
return ans;}

void babuBhaiya()
{
// #ifndef ONLINE_JUDGE
    // freopen("input.txt", "r", stdin);
    // freopen("output.txt", "w", stdout);
// #endif
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
}

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

const int N = 1e5+1;
const double pi = acos(-1);

vi adj[N];
bool visited[N];
int cnt = 0;

void dfs(int node){
    visited[node] = true;
    cnt++;
    for(int x : adj[node]){
        if(!visited[x]){
            dfs(x);
        }
    }
}

void solve(){

    int n, k; cin>>n>>k;
    fo(i,n-1){
        int a, b, c; cin>>a>>b>>c;
        if(c == 0){
            adj[a].pb(b);
            adj[b].pb(a);
        }
    }
    int ans = power(n,k);
    for(int i = 1;i<=n;i++){
        if(!visited[i]){
            cnt = 0;
            dfs(i);
            ans -= power(cnt,k);
        }
    }
    cout<<ans;
}

 
int32_t main()
{
    babuBhaiya();

    int t;

    t = 1;
    //cin>>t;

    while(t--){
        solve();
    }
    
    return 0;
}