#include <stdio.h>

const int Mod = 998244353;
long long fact[100001], fact_inv[100001];

long long div_mod(long long x, long long y, long long z)
{
	if (x % y == 0) return x / y;
	else return (div_mod((1 + x / y) * y - x, (z % y), y) * z + x) / y;
}

long long pow_mod(long long n, int k)
{
	long long N, ans = 1;
	for (N = n; k > 0; k >>= 1, N = N * N % Mod) if (k & 1) ans = ans * N % Mod;
	return ans;
}

long long combination(int n, int k)
{
	return fact[n] * fact_inv[k] % Mod * fact_inv[n-k] % Mod;
}

typedef struct List {
	struct List *next;
	int v;
} list;

int main()
{
	int i, k, N, C, u, w, deg[100001] = {}, num[100001] = {};
	scanf("%d %d", &N, &C);
	if (N == 2) {
	    if (C == 1) printf("1\n");
	    else printf("0\n");
	    fflush(stdout);
	    return 0;
	}
	for (i = 0; i < N - 1; i++) {
		scanf("%d %d", &u, &w);
		deg[u]++;
		deg[w]++;
	}
	for (u = 1; u <= N; u++) num[deg[u]]++;
	for (i = 1, fact[0] = 1; i <= N; i++) fact[i] = fact[i-1] * i % Mod;
	for (i = N - 1, fact_inv[N] = div_mod(1, fact[N], Mod); i >= 0; i--) fact_inv[i] = fact_inv[i+1] * (i + 1) % Mod;
	
	int j, flag;
	long long ans = 0, pow[2][100001], tmp, tmpp, memo[257];
	for (k = 1; k <= C; k++) memo[k] = 1;
	for (k = 1; k <= C; k++) {
		for (i = 1, pow[0][0] = 1, pow[1][0] = 1; i < N; i++) {
			pow[0][i] = pow[0][i-1] * k % Mod;
			pow[1][i] = pow[1][i-1] * (k - 1) % Mod;
		}
		for (i = 2, flag = 0; i < N; i++) {
			if (num[i] == 0) continue;
			tmp = pow[0][i];
			for (j = i / 2 + 1; j < i; j++) tmp += Mod - pow[1][i-j] * combination(i, j) % Mod * k % Mod;
			tmp %= Mod;
			
			if (flag == 0) {
				flag = 1;
				memo[k] = memo[k] * tmp % Mod;
				tmpp = pow_mod(div_mod(tmp, k, Mod), num[i] - 1);
				memo[k] = memo[k] * tmpp % Mod;
			} else {
				tmpp = pow_mod(div_mod(tmp, k, Mod), num[i]);
				memo[k] = memo[k] * tmpp % Mod;
			}
		}
	}
	for (k = 1; k <= C; k++) {
		if ((k + C) % 2 == 0) ans += memo[k] * combination(C, k) % Mod;
		else ans += Mod - memo[k] * combination(C, k) % Mod;
	}
	printf("%lld\n", ans % Mod);
	fflush(stdout);
	return 0;
}