4873：ZCC Loves Intersection

题目描述

After beats all opponents in 3-dimension-world OI, ZCC feels bored and sets about going to other universes. In a universe with D dimension(s), ZCC finds D segments floating in the air. To be more precise: if we build a rectangular coordinate system with D axis, each of the segments is parallel with one axis, whose endpoints have a coordination of which all components belong to the set {x∈Z|0≤x＜N}. For each axis, there is exactly one segment parallel with it.
Each of the D segments changes location every second. Read the pseudo code below for more details:

Every second, from every pair of segments intersect, ZCC acquires a unit of Energy. Calculate the Expectation of the amount of the acquired energy per second please.

输入解释

There are several test cases in one input file. EOF indicates the end of input file.
Every test case contain two positive numbers N, D in one line.
It is guaranteed that 1＜N≤10^9, D≤99. The number of test cases≤10.

输出解释

For each test case, output a line with an integer or an irreducible fraction p/q, which is the Expectation.

输入样例

2 2
3 3
5 5

输出样例

1
49/81
18/625

提示

For the first test case of the sample input, there are 2 segments in a 2*2 lattice.
Because two endpoint couldn’t coincide, two segments must be (0,y)-(1,y) and (x,0)-(x,1). (x, y∈{0,1}) 
Thus, they always intersect at (x,y). As an irreducible fraction the answer is 1/1, where q = 1, so we should output an integer 1 instead.

来自杭电HDUOJ的附加信息

Author	镇海中学
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该题目是Virtual Judge题目，来自杭电HDUOJ

题目来源 2014 Multi-University Training Contest 2

源链接： HDU-4873

最后修改于 2020-10-25T23:17:39+00:00 由爬虫自动更新

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通过率 --%

时间上限	内存上限
2000/1000MS(Java/Others)	131072/131072K(Java/Others)