【cf437D】The Child and Zoo

2014年6月1日1,4334

Of course our child likes walking in a zoo. The zoo has n areas, that are numbered from 1 to n. The i-th area contains ai animals in it. Also there are m roads in the zoo, and each road connects two distinct areas. Naturally the zoo is connected, so you can reach any area of the zoo from any other area using the roads.

Our child is very smart. Imagine the child want to go from area p to area q. Firstly he considers all the simple routes from p to q. For each route the child writes down the number, that is equal to the minimum number of animals among the route areas. Let’s denote the largest of the written numbers asf(p, q). Finally, the child chooses one of the routes for which he writes down the value f(p, q).

After the child has visited the zoo, he thinks about the question: what is the average value of f(p, q) for all pairs p, q (p ≠ q)? Can you answer his question?

Input

The first line contains two integers n and m (2 ≤ n ≤ 105; 0 ≤ m ≤ 105). The second line contains nintegers: a1, a2, …, an (0 ≤ ai ≤ 105). Then follow m lines, each line contains two integers xi and yi(1 ≤ xi, yi ≤ n; xi ≠ yi), denoting the road between areas xi and yi.

All roads are bidirectional, each pair of areas is connected by at most one road.

Output

Output a real number — the value of .

The answer will be considered correct if its relative or absolute error doesn’t exceed 10 - 4.

Sample test(s)
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output

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output

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Note

Consider the first sample. There are 12 possible situations:

  • p = 1, q = 3, f(p, q) = 10.
  • p = 2, q = 3, f(p, q) = 20.
  • p = 4, q = 3, f(p, q) = 30.
  • p = 1, q = 2, f(p, q) = 10.
  • p = 2, q = 4, f(p, q) = 20.
  • p = 4, q = 1, f(p, q) = 10.

Another 6 cases are symmetrical to the above. The average is .

Consider the second sample. There are 6 possible situations:

  • p = 1, q = 2, f(p, q) = 10.
  • p = 2, q = 3, f(p, q) = 20.
  • p = 1, q = 3, f(p, q) = 10.

Another 3 cases are symmetrical to the above. The average is .

题解

并查集。。。蛋碎一地

 

  • Mektpoy2014年6月2日 上午12:56 回复

    噗 这个题不是省冬就讲过了吗 涨分好题您都不做

    #1  
    • hzwer2014年6月2日 上午9:04 回复
      admin

      啥省冬讲过!?

      #11
      • Mektpoy2014年6月2日 下午4:05 回复

        是啊 省冬原题

        #12
        • hzwer2014年6月3日 上午11:45 回复
          admin

          表示当时我根本听不懂……

          #13