rt，似乎是李超树的部分错了

#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
#include <algorithm>

using namespace std;

//#define getchar() (p1 == p2 && (p2 = (p1 = buf) + fread(buf , 1 , 1 << 21 , stdin) , p1 == p2) ? EOF :*p1++)
//char buf[1 << 21], *p1 = buf, *p2 = buf;

inline int read() {
	register char c = getchar();
	register int x = 0, f = 1;
	while(c < '0' || c > '9') {
		if (c == '-')
			f = -1;
		c = getchar();
	}
	while(c >= '0' && c <= '9') {
		x = (x << 3) + (x << 1) + c - 48;
		c = getchar();
	}
	return x * f;
}


#define lll long long

const int N = 1e5 + 5;
const lll inf = 123456789123456789ll;

int n , m;

struct node{
	int to , next , w;
}e[N << 1];

int head[N] , cnt = 0;

inline void add(int x , int y , int w , int z = 1){
	e[++cnt].next = head[x];
	e[cnt].to = y;
	e[cnt].w = w;
	head[x] = cnt;
	if(z)
		add(y , x , w , 0);
}

int siz[N] , fa[N] , dep[N] , dfn[N] , top[N] , dcnt = 0 , son[N] , rk[N];

lll dis[N];

struct SegTree{
	lll k[N << 2] , b[N << 2];
	lll mn[N << 2] , ll[N << 2] , rr[N << 2] , mx[N << 2];
	
	void update(int x){
		mn[x] = min(mn[x] , min(mn[x << 1] , mn[x << 1 | 1]));
	}
	
	void build(int x , int l , int r){
		b[x] = mn[x] = inf;
		ll[x] = dis[rk[l]];
		rr[x] = dis[rk[r]];
		if(l == r)
			return;
		int mid = (l + r) >> 1;
		mx[x] = dis[rk[mid]];
		build(x << 1 , l , mid);
		build(x << 1 | 1 , mid + 1 , r);
	}
	
	void modify(int x , int l , int r , int ql , int qr , lll K , lll B){
		if(l > qr || r < ql)
			return;
		if(l >= ql && r <= qr){
			lll L = ll[x] , R = rr[x];
			lll x0 = k[x] * L + b[x];
			lll y0 = k[x] * R + b[x];
			lll x1 = K * L + B;
			lll y1 = K * R + B;
			if(x1 >= x0 && y0 <= y1)
				return;
			if(x0 >= x1 && y1 <= y0){
				k[x] = K;
				b[x] = B;
				mn[x] = min(mn[x] , min(x1 , y1));
				return;
			}
			int mid = (l + r) >> 1;
			lll Mx = mx[x];
			double p = 1.0 * (b[x] - B) / (K - k[x]);
			if(x0 < x1){
				if(p <= (double)Mx){
					modify(x << 1 , l , mid , ql , qr , k[x] , b[x]);
					k[x] = K;
					b[x] = B;
				}
				else
					modify(x << 1 | 1 , mid + 1 , r , ql , qr , K , B);
			}
			else{
				if(p <= (double)Mx)
					modify(x << 1 , l , mid , ql , qr , K , B);
				else{
					modify(x << 1 | 1 , mid + 1 , r , ql , qr , k[x] , b[x]);
					k[x] = K;
					b[x] = B;
				}
			}
			mn[x] = min(mn[x] , min(x1 , y1));
			update(x);
			return;
		}
		int mid = (l + r) >> 1;
		modify(x << 1 , l , mid , ql , qr , K , B);
		modify(x << 1 | 1 , mid + 1 , r , ql , qr , K , B);
		update(x);
	}
	
	lll query(int x , int l , int r , int ql , int qr){
		if(l > qr || r < ql)
			return inf;
		if(l >= ql && r <= qr)
			return mn[x];
		lll res = inf;
		if(b[x] != inf){
			lll L = max(l , ql);
			lll R = min(r , qr);
			res = min(k[x] * dis[rk[L]] , k[x] * dis[rk[R]]) + b[x];
		}
		int mid = (l + r) >> 1;
		res = min(res , query(x << 1 , l , mid , ql , qr));
		res = min(res , query(x << 1 | 1 , mid + 1 , r , ql , qr));
		return res;
	}
	
}Tr;

void dfs1(int u , int f){
	siz[u] = 1;
	for(int i = head[u]; i; i = e[i].next){
		int v = e[i].to;
		if(v == f)
			continue;
		fa[v] = u;
		dep[v] = dep[u] + 1;
		dis[v] = dis[u] + e[i].w;
		dfs1(v , u);
		siz[u] += siz[v];
		if(siz[v] > siz[son[u]])
			son[u] = v;
	}
}

void dfs2(int u){
	if(u == son[fa[u]])
		top[u] = top[fa[u]];
	else
		top[u] = u;
	dfn[u] = ++dcnt;
	rk[dcnt] = u;
	for(int i = head[u]; i; i = e[i].next){
		int v = e[i].to;
		if(v == fa[u])
			continue;
		dfs2(v);
	}
}

int lca(int x , int y){
	while(top[x] != top[y]){
		if(dep[top[x] > dep[top[y]]])
			x = fa[top[x]];
		else
			y = fa[top[y]];
	}
	if(dep[x] < dep[y])
		return x;
	else
		return y;
}

void modify(int u , int v , lll K , lll B){
	while(top[u] != top[v]){
		Tr.modify(1 , 1 , n , dfn[top[u]] , dfn[u] , K , B);
		u = fa[top[u]];
	}
	Tr.modify(1 , 1 , n , dfn[v] , dfn[u] , K , B);
}

lll query(int u  , int v){
	lll res = inf;
	while(top[u] != top[v]){
		if(dep[top[u]] < dep[top[v]])
			swap(u , v);
			res = min(res , Tr.query(1 , 1 , n , dfn[top[u]] , dfn[u]));
			u = fa[top[u]];
	}
	if(dep[u] > dep[v])
		swap(u , v);
	res = min(res , Tr.query(1 , 1 , n , dfn[u] , dfn[v]));
	return res;
}

int main(){
	scanf("%d%d" , &n , &m);
	for(int i = 1; i < n; i++){
		int u , v , w;
		u = read();
		v = read();
		w = read();
//		scanf("%d%d%d" , &u , &v , &w);
		add(u , v , w);
	}
	dfs1(1 , 0);
	dfs2(1);
//	cout << "fuck you" << endl;
//	for(int i = 1; i <= n; i++){
//		cout << siz[i] << " " << son[i] << " " << dep[i] << " " << dis[i] << " " << dfn[i] << " " << rk[i] << endl;;		
//	}
	Tr.build(1 , 1 , n);
	while(m--){
		int opt;
		opt = read();
//		scanf("%d" , &opt);
		if(opt == 1){
			int u , v , K , B;
			u = read();
			v = read();
			K = read();
			B = read();
//			scanf("%d%d%d%d" , &u , &v , &K , &B);
			int LCA = lca(u , v);
			modify(u , LCA , -K , dis[u] * K + B);
			modify(v , LCA , K , (dis[u] - 2 * dis[LCA]) * K + B);
		}
		else{
			int u , v;
			u = read();
			v = read();
//			scanf("%d%d" , &u , &v);
			printf("%lld\n" , query(u , v));	
		}
	}
	return 0;
}