# [USACO07NOV] Cow Relays G

## 题意翻译

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 $1\le u,v\le 1000$，$1\le w\le 1000$。

## 题目描述

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。

## 输入输出格式

### 输入格式

\* 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

### 输出格式

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

## 输入输出样例

### 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

`10`