## 题目描述

For their physical fitness program, N ($2 ≤ N ≤ 1000000$) 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 ($1 ≤ I1_i ≤ 1000$; $1 ≤ I2_i ≤1000$ ), each of which is the termination for at least two trails. The cows know the lengthi of each trail ($1 ≤ length_i ≤ 1000$), 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.

## 输入输出格式

• 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: $length_i$ , $I1_i$ , and $I2i$

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

## 题解

$f_{k,i,j}$表示$i->j$ 走 $k$ 条路的最小值。