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Posted By: silversplash   2/18/2007 2:19:00 PM
Hey everyone , this is a problem i am trying to work out
. I am trying to use a dynamic solution somewhat like the coins , knapsack etc. problems . DOES ANYONE HAVE ANY SUGGESTIONS OR POSSILBE SOLUTIONS ? HOPE U ALL RESPOND ,THANKS


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.

Input format
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 comprise the set S.

Sample input
4 19
2 3 5 7

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

Sample output

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