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Language: Slim Span
Description Given an undirected weighted graph The graph E is a set of undirected edges {e_{1}, e_{2}, …, e}. Each edge _{m}e ∈ E has its weight w(e).A spanning tree Figure 5: A graph G and the weights of the edgesFor example, a graph Figure 6: Examples of the spanning trees of GThere are several spanning trees for T is 4. The slimnesses of spanning trees _{a}T, _{b}T and _{c}T shown in Figure 6(b), (c) and (d) are 3, 2 and 1, respectively. You can easily see the slimness of any other spanning tree is greater than or equal to 1, thus the spanning tree Td in Figure 6(d) is one of the slimmest spanning trees whose slimness is 1._{d}Your job is to write a program that computes the smallest slimness. Input The input consists of multiple datasets, followed by a line containing two zeros separated by a space. Each dataset has the following format.
Every input item in a dataset is a non-negative integer. Items in a line are separated by a space. n is the number of the vertices and m the number of the edges. You can assume 2 ≤ b (_{k}k = 1, …, m) are positive integers less than or equal to n, which represent the two vertices v and _{ak}v connected by the _{bk}kth edge e. _{k}w is a positive integer less than or equal to 10000, which indicates the weight of _{k}e. You can assume that the graph _{k}G = (V, E) is simple, that is, there are no self-loops (that connect the same vertex) nor parallel edges (that are two or more edges whose both ends are the same two vertices).Output For each dataset, if the graph has spanning trees, the smallest slimness among them should be printed. Otherwise, −1 should be printed. An output should not contain extra characters. Sample Input 4 5 1 2 3 1 3 5 1 4 6 2 4 6 3 4 7 4 6 1 2 10 1 3 100 1 4 90 2 3 20 2 4 80 3 4 40 2 1 1 2 1 3 0 3 1 1 2 1 3 3 1 2 2 2 3 5 1 3 6 5 10 1 2 110 1 3 120 1 4 130 1 5 120 2 3 110 2 4 120 2 5 130 3 4 120 3 5 110 4 5 120 5 10 1 2 9384 1 3 887 1 4 2778 1 5 6916 2 3 7794 2 4 8336 2 5 5387 3 4 493 3 5 6650 4 5 1422 5 8 1 2 1 2 3 100 3 4 100 4 5 100 1 5 50 2 5 50 3 5 50 4 1 150 0 0 Sample Output 1 20 0 -1 -1 1 0 1686 50 Source |

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