[USACO07NOV] Cow Relays G


给定一张 $T$ 条边的无向连通图,求从 $S$ 到 $E$ 经过 $N$ 条边的最短路长度。 ### 输入格式 第一行四个正整数 $N,T,S,E$ ,意义如题面所示。 接下来 $T$ 行每行三个正整数 $w,u,v$ ,分别表示路径的长度,起点和终点。 ### 输出格式 一行一个整数表示图中从 $S$ 到 $E$ 经过 $N$ 条边的最短路长度。 ### 数据范围 对于所有的数据,保证 $1\le N\le 10^6$,$2\le T\le 100$。 所有的边保证 $1\le u,v\le 1000$,$1\le w\le 1000$。


For their physical fitness program, N (2 ≤ N ≤ 1,000,000) cows have decided to run a relay race using the T (2 ≤ T ≤ 100) cow trails throughout the pasture. Each trail connects two different intersections (1 ≤ I1i ≤ 1,000; 1 ≤ I2i ≤ 1,000), each of which is the termination for at least two trails. The cows know the lengthi of each trail (1 ≤ lengthi  ≤ 1,000), the two intersections the trail connects, and they know that no two intersections are directly connected by two different trails. The trails form a structure known mathematically as a graph. To run the relay, the N cows position themselves at various intersections (some intersections might have more than one cow). They must position themselves properly so that they can hand off the baton cow-by-cow and end up at the proper finishing place. Write a program to help position the cows. Find the shortest path that connects the starting intersection (S) and the ending intersection (E) and traverses exactly N cow trails. 给出一张无向连通图,求S到E经过k条边的最短路。



\* Line 1: Four space-separated integers: N, T, S, and E \* Lines 2..T+1: Line i+1 describes trail i with three space-separated integers: lengthi , I1i , and I2i


\* Line 1: A single integer that is the shortest distance from intersection S to intersection E that traverses exactly N cow trails.


输入样例 #1

2 6 6 4
11 4 6
4 4 8
8 4 9
6 6 8
2 6 9
3 8 9

输出样例 #1