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.

* 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}

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