class LazySegmentTree: def __init__( self, n, indentity_e_node, indentity_e_lazy, combine_node_f, combine_lazy_f, reflect_f, ): self._n = n self._size = 1 self._height = 0 while self._size < self._n: self._size <<= 1 self._height += 1 self._indentity_e_node = indentity_e_node self._indentity_e_lazy = indentity_e_lazy self._combine_node_f = combine_node_f self._combine_lazy_f = combine_lazy_f self._reflect_f = reflect_f self._node = [self._indentity_e_node] * (2 * self._size) self._lazy = [self._indentity_e_lazy] * (2 * self._size) #遅延データの値を値データに反映させたときの値を返す。 def _reflect_lazy(self, index): return self._reflect_f(self._node[index], self._lazy[index])%mod def _propagate_from_top(self, index): index += self._size for h in range(self._height, 0, -1): i = index >> h if self._lazy[i] != self._indentity_e_lazy: self._lazy[i << 1] = self._combine_lazy_f( self._lazy[i << 1], self._lazy[i] )%mod self._lazy[i << 1 | 1] = self._combine_lazy_f( self._lazy[i << 1 | 1], self._lazy[i] )%mod self._node[i] = self._reflect_lazy(i) self._lazy[i] = self._indentity_e_lazy def _update_from_bottom(self, index): index = (index + self._size) >> 1 while index: self._node[index] = self._combine_node_f( self._reflect_lazy(index << 1), self._reflect_lazy(index << 1 | 1) )%mod index >>= 1 def build(self, array): assert len(array) == self._n for index, value in enumerate(array, start=self._size): self._node[index] = value for index in range(self._size - 1, 0, -1): self._node[index] = self._combine_node_f( self._node[index << 1], self._node[index << 1 | 1] ) # 区間更新 位置[L, R) (0-indexed)を値valueで更新 def update(self, L, R, value): self._propagate_from_top(L) self._propagate_from_top(R - 1) L_lazy = L + self._size R_lazy = R + self._size while L_lazy < R_lazy: if L_lazy & 1: self._lazy[L_lazy] = self._combine_lazy_f(self._lazy[L_lazy], value) self._lazy[L_lazy] %= mod L_lazy += 1 if R_lazy & 1: R_lazy -= 1 self._lazy[R_lazy] = self._combine_lazy_f(self._lazy[R_lazy], value) self._lazy[R_lazy] %= mod L_lazy >>= 1 R_lazy >>= 1 self._update_from_bottom(L) self._update_from_bottom(R - 1) # 区間取得 区間[L, R) (0-indexed)内の要素について # L番目から順にcombine_node_fを適用した値を返す。 def fold(self, L, R): self._propagate_from_top(L) self._propagate_from_top(R - 1) L += self._size R += self._size value_L = self._indentity_e_node value_R = self._indentity_e_node while L < R: if L & 1: value_L = self._combine_node_f(value_L, self._reflect_lazy(L)) value_L %= mod L += 1 if R & 1: R -= 1 value_R = self._combine_node_f(value_R, self._reflect_lazy(R)) value_R %= mod L >>= 1 R >>= 1 return self._combine_node_f(value_L, value_R) N, K = map(int, input().split()) inv = [1] * (N + 1) mod = 998244353 for i in range(1, N + 1): inv[i] = pow(i, mod - 2, mod) # pre = [0] * (N + 1) # pre[0] = 1 pre = LazySegmentTree(N + 1, 0, 0, max, lambda x, y:x+y, lambda x, y:x+y) ans = 0 pre.update(0, 1, 1) for k in range(K): now = LazySegmentTree(N + 1, 0, 0, max, lambda x, y:x+y, lambda x, y:x+y) for i in range(N): # for j in range(i + 1, N + 1): # now[j] += inv[N - i] * pre[i] now.update(i + 1, N + 1, inv[N - i] * pre.fold(i, i + 1) % mod) ans += now.fold(N, N + 1) ans %= mod pre, now = now, pre print(ans)