#include <bits/stdc++.h>   using namespace std;   inline long long read() {     long long x = 0;     bool pos = 1;     char ch = getchar();     for (; !isdigit(ch); ch = getchar())       if (ch ==  - ) pos = 0;     for (; isdigit(ch); ch = getchar()) x = x * 10 + ch -  0 ;     return pos ? x : -x;   }   const int N = 1 << 18 | 2, M = N;   const int mod = 998244353, G = 3;   int sz[N], dep[N];   vector<int> v[N];   inline int ksm(int a, int b) {     int ans = 1;     for (; b; b >>= 1) {       if (b & 1) ans = (long long)ans * a % mod;       a = (long long)a * a % mod;     }     return ans;   }   struct ffter {     int wn[N], rev[N];     void init(int n) {       int t = 1, L = 0;       while (t < n) {         t <<= 1;         L++;       }       int w = ksm(G, (mod - 1) / n);       for (int i = wn[0] = 1; i < n; i++) {         wn[i] = (long long)wn[i - 1] * w % mod;         rev[i] = rev[i >> 1] >> 1 | ((i & 1) << (L - 1));       }     }     void zheng(vector<int> &a) {       for (auto &i : a) i = (i + mod) % mod;     }     void dft(vector<int> &a) {       int n = a.size();       zheng(a);       for (int i = 0; i < n; i++)         if (rev[i] < i) swap(a[rev[i]], a[i]);       for (int i = 1; i < n; i <<= 1) {         for (int j = 0; j < n; j += i << 1) {           for (int k = j, l = 0; l < i; k++, l++) {             long long t = (long long)wn[l * (n / (i << 1))] * a[k + i] % mod;             a[k + i] = (a[k] < t) ? a[k] - t + mod : a[k] - t;             a[k] = a[k] + t >= mod ? a[k] + t - mod : a[k] + t;           }         }       }     }     void idft(vector<int> &a) {       int n = a.size();       dft(a);       reverse(a.begin() + 1, a.end());       int zs = ksm(n, mod - 2);       for (auto &i : a) i = (long long)i * zs % mod;     }   } T;   void FFT(vector<int> &a, vector<int> &b) {     int n = a.size() + b.size() - 1;     int len = 1;     while (len < n) len <<= 1;     T.init(len);     a.resize(len);     b.resize(len);     T.dft(a);     T.dft(b);     for (int i = 0; i < len; i++) a[i] = (long long)a[i] * b[i] % mod;     T.idft(a);     a.resize(n);   }   int n, son[N];   vector<int> tr[M], Tr[M], dp[N], f[N];   void solve(int p);   void zy(vector<int> &a, int len) {     a.resize(a.size() + len);     for (int i = a.size() - 1; i >= len; i--) a[i] = a[i - len];     for (int i = 0; i < len; i++) a[i] = 0;   }   void bao(int p, int son) {     for (auto i : v[p])       if (dep[i] > dep[p] && i != son) solve(i);   }   vector<int> get(int p, int son) {     priority_queue<pair<int, vector<int> > > q;     while (q.size()) q.pop();     for (auto i : v[p])       if (dep[i] > dep[p] && i != son) {         q.push(make_pair(-dp[i].size(), dp[i]));       }     if (q.size() == 0) {       vector<int> jb(1);       jb[0] = 1;       return jb;     }     while (q.size() > 1) {       vector<int> a = q.top().second;       q.pop();       vector<int> b = q.top().second;       q.pop();       FFT(a, b);       q.push(make_pair(-a.size(), a));     }     vector<int> jb = q.top().second;     q.pop();     return jb;   }   vector<int> operator+(vector<int> a, vector<int> b) {     if (a.size() < b.size()) swap(a, b);     for (unsigned i = 0; i < b.size(); i++) a[i] = (a[i] + b[i]) % mod;     return a;   }   int TOT;   void bao(int l, int r, int nod) {     if (l == r) {       tr[nod] = f[l];       if (r == TOT) {         Tr[nod] = tr[nod];         zy(Tr[nod], 1);       } else         Tr[nod].resize(1);       Tr[nod][0] = 1;       return;     }     int mid = (l + r) >> 1;     bao(l, mid, nod << 1);     bao(mid + 1, r, nod << 1 | 1);     tr[nod] = tr[nod << 1];     FFT(tr[nod], tr[nod << 1 | 1]);     FFT(Tr[nod << 1 | 1], tr[nod << 1]);     zy(Tr[nod << 1 | 1], mid - l + 1);     Tr[nod] = Tr[nod << 1] + Tr[nod << 1 | 1];   }   void solve(int p) {     int tot = 0, jb = 0;     for (int i = p; i; i = son[i]) bao(i, son[i]);     for (int i = p; i; i = son[i]) {       f[++tot] = get(i, son[i]);     }     for (int i = 1; i <= tot; i++) jb += f[i].size();     TOT = tot;     bao(1, tot, 1);     dp[p] = Tr[1];   }   void init(int p, int fa) {     sz[p] = 1;     dep[p] = dep[fa] + 1;     for (auto i : v[p])       if (i != fa) {         init(i, p);         sz[p] += sz[i];         if (sz[i] > sz[son[p]]) son[p] = i;       }   }   int main() {     n = read();     int x = read() % mod;     for (int i = 1; i < n; i++) {       int x = read(), y = read();       v[x].push_back(y);       v[y].push_back(x);     }     init(1, 0);     solve(1);     vector<int> ans = dp[1];     ans[0]--;     int dq = 1, Ans = 0;     for (int i = 1; i <= n; i++) {       if (i > 1)         dq = (long long)dq * (i + x - 1) % mod * ksm(i - 1, mod - 2) % mod;       Ans = (Ans + (long long)dq * ans[i]) % mod;     }     cout << (Ans + mod) % mod << endl;   }