Cow Relays

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 7463		Accepted: 2922

Description

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 ≤ I_1i ≤ 1,000; 1 ≤ I_2i ≤ 1,000), each of which is the termination for at least two trails. The cows know the length_i of each trail (1 ≤ length_i  ≤ 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.

Input

* 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 , I_1i , and I_2i

Output

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

Sample Input

2 6 6 411 4 64 4 88 4 96 6 82 6 93 8 9

Sample Output

10

#include 
     
      #include 
      
       #include 
       
        #include 
        
         #include 
         
          using namespace std;const int maxn=1005;const int inf=1e9;int mp[maxn][maxn];int tmp[maxn][maxn];int mmp[maxn][maxn];int res[maxn][maxn];int cord[maxn];bool used[maxn];int n,m,st,ed;int num;void init(){    for(int i=0;i
          
           b[cord[i]][cord[k]]+c[cord[k]][cord[j]]) a[cord[i]][cord[j]]=b[cord[i]][cord[k]]+c[cord[k]][cord[j]];}void trans(int a[][maxn],int b[][maxn]){ for(int i=0;i
           
            >=1; }}int main(){ scanf("%d %d %d %d",&n,&m,&st,&ed); init(); for(int i=0;i