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| /* vegetable1024 | Maybe Lovely? */
#include <bits/stdc++.h> #define maxn 800005 #define int long long #define lson(x) (x << 1) #define rson(x) (x << 1 | 1) using namespace std;
//DEBUG TEMPLATE template<typename T> void Print(T value){ std::cout << value << '\n'; } template<typename Head, typename... Rail> void Print(Head head, Rail... rail){ std::cout << head << ", "; Print(rail...); }
int read(){ int x = 0; char ch = getchar(); while(ch < '0' || ch > '9') ch = getchar(); while(ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar(); return x; }
int qpow(int a, int b, int m){ if(b == 0) return 1; int tmp = qpow(a, b / 2, m); tmp = (tmp * tmp) % m; if(b & 1) tmp = (tmp * a) % m; return tmp; }
const int mod = 998244353; //维护区间欧拉函数的和,支持区间乘法 struct SegTreeSum{ struct Node{ int lf, rt, sum, lazy; } t[maxn]; void Pushdown(int now){ if(t[now].lazy > 1){ t[lson(now)].lazy = (t[now].lazy * t[lson(now)].lazy) % mod; t[rson(now)].lazy = (t[now].lazy * t[rson(now)].lazy) % mod; t[lson(now)].sum = (t[now].lazy * t[lson(now)].sum) % mod; t[rson(now)].sum = (t[now].lazy * t[rson(now)].sum) % mod; t[now].lazy = 1; } } void Pushup(int now){ t[now].sum = (t[lson(now)].sum + t[rson(now)].sum) % mod; } void Build(int now, int lf, int rt){ t[now].lf = lf; t[now].rt = rt; if(lf == rt){ t[now].sum = t[now].lazy = 1; return; } t[now].lazy = 1; int mid = (lf + rt) / 2; Build(lson(now), lf, mid); Build(rson(now), mid + 1, rt); Pushup(now); } void Update(int now, int lf, int rt, int k){ if(t[now].lf >= lf && t[now].rt <= rt){ t[now].sum = (t[now].sum * k) % mod; t[now].lazy = (t[now].lazy * k) % mod; return; } if(t[now].lf > rt || t[now].rt < lf){ return; } Pushdown(now); Update(lson(now), lf, rt, k); Update(rson(now), lf, rt, k); Pushup(now); } int Query(int now, int lf, int rt){ if(t[now].lf >= lf && t[now].rt <= rt){ return t[now].sum; } if(t[now].lf > rt || t[now].rt < lf){ return 0; } Pushdown(now); return (Query(lson(now), lf, rt) + Query(rson(now), lf, rt)) % mod; } } smt; //计算每个质因子的出现次数最大值和最小值,判断是否要暴力更新 struct SegTreeRM{ struct Node{ int lf, rt, minn, maxx, lazy; } t[maxn]; void Pushup(int now){ t[now].maxx = max(t[lson(now)].maxx, t[rson(now)].maxx); t[now].minn = min(t[lson(now)].minn, t[rson(now)].minn); } void Pushdown(int now){ if(t[now].lazy){ t[lson(now)].lazy += t[now].lazy; t[rson(now)].lazy += t[now].lazy; t[lson(now)].maxx += t[now].lazy; t[rson(now)].maxx += t[now].lazy; t[lson(now)].minn += t[now].lazy; t[rson(now)].minn += t[now].lazy; t[now].lazy = 0; } } void Build(int now, int lf, int rt){ t[now].lf = lf; t[now].rt = rt; if(lf == rt){ t[now].maxx = t[now].minn = t[now].lazy = 0; return; } int mid = (lf + rt) / 2; Build(lson(now), lf, mid); Build(rson(now), mid + 1, rt); Pushup(now); } void Update(int now, int lf, int rt, int p, int c){ if(t[now].lf >= lf && t[now].rt <= rt){ if(t[now].maxx == 0){ t[now].maxx += c; t[now].minn += c; t[now].lazy += c; smt.Update(1, t[now].lf, t[now].rt, ((p - 1) * qpow(p, c - 1, mod)) % mod); } else if(t[now].minn > 0){ t[now].maxx += c; t[now].minn += c; t[now].lazy += c; smt.Update(1, t[now].lf, t[now].rt, qpow(p, c, mod)); } else{ Pushdown(now); Update(lson(now), lf, rt, p, c); Update(rson(now), lf, rt, p, c); Pushup(now); } return; } if(t[now].lf > rt || t[now].rt < lf){ return; } Pushdown(now); Update(lson(now), lf, rt, p, c); Update(rson(now), lf, rt, p, c); Pushup(now); } } tr[30];
int n, m, xi[maxn]; bool check(int val){ if(val == 1) return false; for(int i = 2; i * i <= val; i++) if(val % i == 0) return false; return true; } int cnt, pri[maxn]; void initp(int lim){ for(int i = 1; i <= lim; i++) if(check(i)) pri[++cnt] = i; smt.Build(1, 1, n); for(int i = 1; i <= cnt; i++) tr[i].Build(1, 1, n); } void De(int l, int r, int w){ for(int i = 1; i <= cnt && w > 1; i++){ int p = pri[i], c = 0; while(w % pri[i] == 0){ w /= pri[i]; c++; } if(c) tr[i].Update(1, l, r, p, c); } } signed main(void) { n = read(); m = read(); initp(100); for(int i = 1; i <= n; i++) xi[i] = read(); for(int i = 1; i <= n; i++) De(i, i, xi[i]); for(int i = 1; i <= m; i++) { int ty = read(); if(ty == 0){ int l = read(), r = read(), w = read(); De(l, r, w); } else{ int l = read(), r = read(); printf("%lld\n", smt.Query(1, l, r)); } } return 0; }
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