题目描述

For a given set of K prime numbers S = {p1, p2, ..., pK}, consider the set of all numbers whose prime factors are a subset of S. This set contains, for example, p1, p1p2, p1p1, and p1p2p3 (among others). This is the set of `humble numbers' for the input set S. Note: The number 1 is explicitly declared not to be a humble number.

Your job is to find the Nth humble number for a given set S. Long integers (signed 32-bit) will be adequate for all solutions.

输入格式

Line 1:    Two space separated integers: K and N, 1 <= K <=100 and 1 <= N <= 100,000.
Line 2:    K space separated positive integers that compose the set S.

输出格式

The Nth humble number from set S printed alone on a line.

样例数据

input

4 19
2 3 5 7

output

27