508. Black-white balls

Time limit per test: 0.25 second(s)
Memory limit: 262144 kilobytes
input: standard
output: standard

n black and white balls were put into a bag. Petya doesn't know exactly how many black balls are there among them. He knows, however, that there are 0, 1,..., n black balls among all balls in the bag with equal probability.

Petya took l balls from the bag at random, and l1 of them turned out black, while l2 other turned out white (l1 + l2 = l). Now he wants to predict how many black balls were there initially in the bag. Of course, if l < n, he can't be sure in his prediction, but he wants to predict a segment [a, b], such that the amount k of black balls belongs to it with probability at least p.

You are given n, l1, l2 and p, and you must find such a and b that b - a is minimal possible. If there are several such pairs (a, b), choose the one with the smallest a.

Input
In the first line there are four integer numbers: 1 ≤ n ≤ 50 — the number of balls in the bag, 0 ≤ l1n — the number of black balls out of the l balls that Petya took from the bag, 0 ≤ l2n - l1 — the number of white balls that Petya took from the bag, 0 ≤ p ≤ 100 — the required confidence in percent.

Output
Output numbers a and b separated by a space, 0 ≤ abn.

Example(s)
sample input
sample output
50 1 24 100
1 26

sample input
sample output
50 1 49 100
1 1

sample input
sample output
50 1 10 95
1 15




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