# https://yukicoder.me/problems/no/3492 import math MIN_VALUE = - 10 ** 18 class CombinationCalculator: """ modを考慮したPermutation, Combinationを計算するためのクラス """ def __init__(self, size, mod): self.mod = mod self.factorial = [0] * (size + 1) self.factorial[0] = 1 for i in range(1, size + 1): self.factorial[i] = (i * self.factorial[i - 1]) % self.mod self.inv_factorial = [0] * (size + 1) self.inv_factorial[size] = pow(self.factorial[size], self.mod - 2, self.mod) for i in reversed(range(size)): self.inv_factorial[i] = ((i + 1) * self.inv_factorial[i + 1]) % self.mod def calc_combination(self, n, r): if n < 0 or n < r or r < 0: return 0 if r == 0 or n == r: return 1 ans = self.inv_factorial[n - r] * self.inv_factorial[r] ans %= self.mod ans *= self.factorial[n] ans %= self.mod return ans def calc_permutation(self, n, r): if n < 0 or n < r: return 0 ans = self.inv_factorial[n - r] ans *= self.factorial[n] ans %= self.mod return ans class LazySegmentTree: """ 非再帰版遅延セグメント木。 更新は「加法」、取得は「最大値」のもの限定。 取得のところの都合で取得演算子は可換になっている必要がある。 """ def __init__(self, init_array, max_degree, B): n = 1 while n < len(init_array): n *= 2 self.B = B self.max_degree = max_degree self.size = n self.array = [MIN_VALUE for _ in range(2 * self.size)] self.lazy_array = [[0] * (max_degree + 1) for _ in range(2 * self.size)] for i, a in enumerate(init_array): self.array[self.size + i] = a def _propagates(self, *ids): for i in reversed(ids): self._propagate(i) def _propagate(self, i): v = self.lazy_array[i] if self._is_zero(v): return if i < self.size: for j in range(self.max_degree + 1): self.lazy_array[2 * i][j] += v[j] self.lazy_array[2 * i][j] %= self.B self.lazy_array[2 * i + 1][j] += v[j] self.lazy_array[2 * i + 1][j] %= self.B self._addapt(2 * i, v) self._addapt(2 * i + 1, v) for j in range(self.max_degree + 1): self.lazy_array[i][j] = 0 def _is_zero(self, v): for j in range(self.max_degree + 1): if v[j] != 0: return False return True def _addapt(self, index, v): if index >= self.size: i = index - self.size ans = 0 for j in range(self.max_degree + 1): x = pow(i + 1, j, self.B) x *= v[j] x %= self.B ans += x ans %= self.B self.array[index] += ans self.array[index] %= self.B def _get_target_index(self, l, r): L = l + self.size; R = r + self.size lm = (L // (L & -L)) >> 1 rm = (R // (R & -R)) >> 1 while 0 < L and L < R: if R <= rm: yield R if L <= lm: yield L L >>= 1; R >>= 1 while L > 0: yield L L >>= 1 def add(self, l, r, v): # 2. 区間[l, r)のdata, lazyの値を更新 L = self.size + l; R = self.size + r *ids, = self._get_target_index(l, r) self._propagates(*ids) while L < R: if R & 1: R -= 1 for j in range(self.max_degree + 1): self.lazy_array[R][j] += v[j] self.lazy_array[R][j] %= self.B self._addapt(R, v) if L & 1: for j in range(self.max_degree + 1): self.lazy_array[L][j] += v[j] self.lazy_array[L][j] %= self.B self._addapt(L, v) L += 1 L >>= 1; R >>= 1 # 3. 伝搬させた区間について、ボトムアップにdataの値を伝搬する def get_value(self, m): # 1. トップダウンにlazyの値を伝搬 self._propagates(*self._get_target_index(m, m + 1)) return self.array[self.size + m] def main(): N, B, Q = map(int ,input().split()) queries = [] max_degree = 0 for _ in range(Q): l, m, r, c, d = map(int, input().split()) queries.append((l - 1, m - 1, r - 1, c, d)) max_degree = max(max_degree, d) combi_map = {} def dfs(combi_map, d, j): if (d, j) in combi_map: return combi_map[(d, j)] if d == j or j == 0: x = 1 elif d < 0 or d < j: x = 0 else: x = dfs(combi_map, d - 1, j) + dfs(combi_map, d - 1, j - 1) combi_map[(d, j)] = x return x for d in range(max_degree + 1): for j in range(d + 1): dfs(combi_map, d, j) lazy_seg_tree = LazySegmentTree([0] * N, max_degree, B) for l, m, r, c, d in queries: v = [0] * (max_degree + 1) c %= B if c == 0: v[d] = 1 else: for j in range(d + 1): x = combi_map[(d, j)] x *= pow(c, d - j, B) x %= B v[j] = x lazy_seg_tree.add(l, r + 1, v) ans = lazy_seg_tree.get_value(m) print(ans) if __name__ == "__main__": main()