Problem: You are given a tree of n vertices. You are to select k (not necessarily distinct) simple paths in such a way that it is possible to split all edges of the tree into three sets: edges not contained in any path, edges that are a part of exactly one of these paths, and edges that are parts of all selected paths, and the latter set should be non-empty.

Compute the number of ways to select k paths modulo 998244353.

The paths are enumerated, in other words, two ways are considered distinct if there are such i (1 ≤ i ≤ k) and an edge that the i-th path contains the edge in one way and does not contain it in the other.

Input

The first line contains two integers n and k (1 ≤ n, k ≤ 10^{5}) — the number of vertices in the tree and the desired number of paths.

The next n - 1 lines describe edges of the tree. Each line contains two integers a and b (1 ≤ a, b ≤ n, a ≠ b) — the endpoints of an edge. It is guaranteed that the given edges form a tree.

Output

Print the number of ways to select k enumerated not necessarily distinct simple paths in such a way that for each edge either it is not contained in any path, or it is contained in exactly one path, or it is contained in all k paths, and the intersection of all paths is non-empty. 

As the answer can be large, print it modulo 998244353.

Examples

Input

3 2
1 2
2 3


Output

7


Input

5 1
4 1
2 3
4 5
2 1


Output

10


Input

29 29
1 2
1 3
1 4
1 5
5 6
5 7
5 8
8 9
8 10
8 11
11 12
11 13
11 14
14 15
14 16
14 17
17 18
17 19
17 20
20 21
20 22
20 23
23 24
23 25
23 26
26 27
26 28
26 29


Output

125580756

Note

In the first example the following ways are valid：

  * ((1,2), (1,2)), 
  * ((1,2), (1,3)), 
  * ((1,3), (1,2)), 
  * ((1,3), (1,3)), 
  * ((1,3), (2,3)), 
  * ((2,3), (1,3)), 
  * ((2,3), (2,3)). 



In the second example k=1, so all n ⋅ (n - 1) / 2 = 5 ⋅ 4 / 2 = 10 paths are valid.

In the third example, the answer is ≥ 998244353, so it was taken modulo 998244353, don't forget it!

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
namespace IO {
const int BUFFER_SIZE = 1 << 15;
char input_buffer[BUFFER_SIZE];
int input_pos = 0, input_len = 0;
void _update_input_buffer() {
  input_len = fread(input_buffer, sizeof(char), BUFFER_SIZE, stdin);
  input_pos = 0;
  if (input_len == 0) input_buffer[0] = EOF;
}
inline char next_char(bool advance = true) {
  if (input_pos >= input_len) _update_input_buffer();
  return input_buffer[advance ? input_pos++ : input_pos];
}
template <typename T>
inline void read_int(T &number) {
  bool negative = false;
  number = 0;
  while (!isdigit(next_char(false)))
    if (next_char() == '-') negative = true;
  do {
    number = 10 * number + (next_char() - '0');
  } while (isdigit(next_char(false)));
  if (negative) number = -number;
}
template <typename T, typename... Args>
inline void read_int(T &number, Args &...args) {
  read_int(number);
  read_int(args...);
}
}  // namespace IO
const int MOD = 998244353;
struct mod_int {
  int val;
  mod_int(long long v = 0) {
    if (v < 0) v = v % MOD + MOD;
    if (v >= MOD) v %= MOD;
    val = v;
  }
  static int mod_inv(int a, int m = MOD) {
    int g = m, r = a, x = 0, y = 1;
    while (r != 0) {
      int q = g / r;
      g %= r;
      swap(g, r);
      x -= q * y;
      swap(x, y);
    }
    return x < 0 ? x + m : x;
  }
  explicit operator int() const { return val; }
  mod_int &operator+=(const mod_int &other) {
    val += other.val;
    if (val >= MOD) val -= MOD;
    return *this;
  }
  mod_int &operator-=(const mod_int &other) {
    val -= other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
    return x % m;
    unsigned x_high = x >> 32, x_low = (unsigned)x;
    unsigned quot, rem;
    asm("divl %4\n" : "=a"(quot), "=d"(rem) : "d"(x_high), "a"(x_low), "r"(m));
    return rem;
  }
  mod_int &operator*=(const mod_int &other) {
    val = fast_mod((uint64_t)val * other.val);
    return *this;
  }
  mod_int &operator/=(const mod_int &other) { return *this *= other.inv(); }
  friend mod_int operator+(const mod_int &a, const mod_int &b) {
    return mod_int(a) += b;
  }
  friend mod_int operator-(const mod_int &a, const mod_int &b) {
    return mod_int(a) -= b;
  }
  friend mod_int operator*(const mod_int &a, const mod_int &b) {
    return mod_int(a) *= b;
  }
  friend mod_int operator/(const mod_int &a, const mod_int &b) {
    return mod_int(a) /= b;
  }
  mod_int &operator++() {
    val = val == MOD - 1 ? 0 : val + 1;
    return *this;
  }
  mod_int &operator--() {
    val = val == 0 ? MOD - 1 : val - 1;
    return *this;
  }
  mod_int operator++(int) {
    mod_int before = *this;
    ++*this;
    return before;
  }
  mod_int operator--(int) {
    mod_int before = *this;
    --*this;
    return before;
  }
  mod_int operator-() const { return val == 0 ? 0 : MOD - val; }
  bool operator==(const mod_int &other) const { return val == other.val; }
  bool operator!=(const mod_int &other) const { return val != other.val; }
  mod_int inv() const { return mod_inv(val); }
  mod_int pow(long long p) const {
    assert(p >= 0);
    mod_int a = *this, result = 1;
    while (p > 0) {
      if (p & 1) result *= a;
      a *= a;
      p >>= 1;
    }
    return result;
  }
  friend ostream &operator<<(ostream &stream, const mod_int &m) {
    return stream << m.val;
  }
};
vector<mod_int> inv = {0, 1}, factorial = {1, 1}, inv_factorial = {1, 1};
void prepare_factorials(int maximum) {
  for (int p = 2; p * p <= MOD; p++) assert(MOD % p != 0);
  inv.resize(maximum + 1);
  factorial.resize(maximum + 1);
  inv_factorial.resize(maximum + 1);
  for (int i = 2; i <= maximum; i++) {
    inv[i] = inv[MOD % i] * (MOD - MOD / i);
    factorial[i] = i * factorial[i - 1];
    inv_factorial[i] = inv[i] * inv_factorial[i - 1];
  }
}
mod_int choose(long long n, long long r) {
  if (r < 0 || r > n) return 0;
  return factorial[n] * inv_factorial[r] * inv_factorial[n - r];
}
mod_int inv_choose(long long n, long long r) {
  assert(0 <= r && r <= n);
  return inv_factorial[n] * factorial[r] * factorial[n - r];
}
mod_int permute(long long n, long long k) {
  if (k < 0 || k > n) return 0;
  return factorial[n] * inv_factorial[n - k];
}
mod_int inv_permute(long long n, long long k) {
  assert(0 <= k && k <= n);
  return inv_factorial[n] * factorial[n - k];
}
namespace NTT {
vector<mod_int> roots = {0, 1};
vector<int> bit_reverse;
int max_size = -1;
mod_int root;
bool is_power_of_two(int n) { return (n & (n - 1)) == 0; }
int round_up_power_two(int n) {
  while (n & (n - 1)) n = (n | (n - 1)) + 1;
  return max(n, 1);
}
int get_length(int n) {
  assert(is_power_of_two(n));
  return __builtin_ctz(n);
}
void bit_reorder(int n, vector<mod_int> &values) {
  if ((int)bit_reverse.size() != n) {
    bit_reverse.assign(n, 0);
    int length = get_length(n);
    for (int i = 0; i < n; i++)
      bit_reverse[i] = (bit_reverse[i >> 1] >> 1) + ((i & 1) << (length - 1));
  }
  for (int i = 0; i < n; i++)
    if (i < bit_reverse[i]) swap(values[i], values[bit_reverse[i]]);
}
void find_root() {
  max_size = 1 << __builtin_ctz(MOD - 1);
  root = 2;
  while (!(root.pow(max_size) == 1 && root.pow(max_size / 2) != 1)) root++;
}
void prepare_roots(int n) {
  if (max_size < 0) find_root();
  assert(n <= max_size);
  if ((int)roots.size() >= n) return;
  int length = get_length(roots.size());
  roots.resize(n);
  while (1 << length < n) {
    mod_int z = root.pow(max_size >> (length + 1));
    for (int i = 1 << (length - 1); i < 1 << length; i++) {
      roots[2 * i] = roots[i];
      roots[2 * i + 1] = roots[i] * z;
    }
    length++;
  }
}
void fft_iterative(int N, vector<mod_int> &values) {
  assert(is_power_of_two(N));
  prepare_roots(N);
  bit_reorder(N, values);
  for (int n = 1; n < N; n *= 2)
    for (int start = 0; start < N; start += 2 * n)
      for (int i = 0; i < n; i++) {
        mod_int even = values[start + i];
        mod_int odd = values[start + n + i] * roots[n + i];
        values[start + n + i] = even - odd;
        values[start + i] = even + odd;
      }
}
const int FFT_CUTOFF = 150;
vector<mod_int> mod_multiply(vector<mod_int> left, vector<mod_int> right) {
  int n = left.size();
  int m = right.size();
  if (min(n, m) < FFT_CUTOFF) {
    static const uint64_t ULL_BOUND =
        numeric_limits<uint64_t>::max() - (uint64_t)MOD * MOD;
    vector<uint64_t> result(n + m - 1, 0);
    for (int i = 0; i < n; i++)
      for (int j = 0; j < m; j++) {
        result[i + j] += (uint64_t)((int)left[i]) * ((int)right[j]);
        if (result[i + j] > ULL_BOUND) result[i + j] %= MOD;
      }
    for (uint64_t &x : result)
      if (x >= MOD) x %= MOD;
    return vector<mod_int>(result.begin(), result.end());
  }
  int N = round_up_power_two(n + m - 1);
  left.resize(N);
  right.resize(N);
  bool equal = left == right;
  fft_iterative(N, left);
  if (equal)
    right = left;
  else
    fft_iterative(N, right);
  mod_int inv_N = mod_int(N).inv();
  for (int i = 0; i < N; i++) left[i] *= right[i] * inv_N;
  reverse(left.begin() + 1, left.end());
  fft_iterative(N, left);
  left.resize(n + m - 1);
  return left;
}
vector<mod_int> mod_power(const vector<mod_int> &v, int exponent) {
  assert(exponent >= 0);
  vector<mod_int> result = {1};
  if (exponent == 0) return result;
  for (int k = 31 - __builtin_clz(exponent); k >= 0; k--) {
    result = mod_multiply(result, result);
    if (exponent >> k & 1) result = mod_multiply(result, v);
  }
  return result;
}
vector<mod_int> mod_multiply_all(const vector<vector<mod_int>> &polynomials) {
  if (polynomials.empty()) return {1};
  struct compare_size {
    bool operator()(const vector<mod_int> &x, const vector<mod_int> &y) {
      return x.size() > y.size();
    }
  };
  priority_queue<vector<mod_int>, vector<vector<mod_int>>, compare_size> pq(
      polynomials.begin(), polynomials.end());
  while (pq.size() > 1) {
    vector<mod_int> a = pq.top();
    pq.pop();
    vector<mod_int> b = pq.top();
    pq.pop();
    pq.push(mod_multiply(a, b));
  }
  return pq.top();
}
}  // namespace NTT
int N, K;
vector<vector<int>> adj;
vector<int> subtree_size;
vector<mod_int> dp_sum;
mod_int total;
mod_int compute_dp(const vector<mod_int> &poly) {
  mod_int dp = 0;
  for (int i = 0; i < (int)poly.size(); i++) dp += permute(K, i) * poly[i];
  return dp;
}
mod_int divide_and_compute_dp(const vector<mod_int> &poly, mod_int a) {
  assert(poly.size() > 1);
  mod_int carry = 0, dp = 0;
  for (int i = 0; i < (int)poly.size(); i++) {
    carry = poly[i] - a * carry;
    dp += permute(K, i) * carry;
  }
  assert(carry == 0);
  return dp;
}
vector<mod_int> save_divide;
vector<int> save_seen;
int seen_index = 0;
void dfs(int node, int parent) {
  if (parent >= 0)
    adj[node].erase(find(adj[node].begin(), adj[node].end(), parent));
  vector<vector<mod_int>> polynomials;
  subtree_size[node] = 1;
  dp_sum[node] = 0;
  for (int child : adj[node]) {
    dfs(child, node);
    subtree_size[node] += subtree_size[child];
    total += dp_sum[node] * dp_sum[child];
    dp_sum[node] += dp_sum[child];
    polynomials.push_back({1, subtree_size[child]});
  }
  vector<mod_int> product = NTT::mod_multiply_all(polynomials);
  mod_int dp_node = compute_dp(product);
  dp_sum[node] += dp_node;
  product = NTT::mod_multiply(product, {1, N - subtree_size[node]});
  seen_index++;
  for (int child : adj[node]) {
    int size = subtree_size[child];
    if (save_seen[size] != seen_index) {
      mod_int dp_add = divide_and_compute_dp(product, size);
      save_divide[size] = dp_add;
      save_seen[size] = seen_index;
    }
    total += save_divide[size] * dp_sum[child];
  }
}
int main() {
  IO::read_int(N, K);
  prepare_factorials(max(N, K));
  adj.assign(N, {});
  for (int i = 0; i < N - 1; i++) {
    int a, b;
    IO::read_int(a, b);
    a--;
    b--;
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  if (K == 1) {
    cout << mod_int(N) * mod_int(N - 1) / 2 << '\n';
    return 0;
  }
  subtree_size.resize(N);
  dp_sum.assign(N, 0);
  save_divide.resize(N + 1);
  save_seen.assign(N + 1, -1);
  total = 0;
  dfs(0, -1);
  cout << total << '\n';
}