Vasya and his friends want to cut a chocolate bar to get at least k pieces, while Vasya wants to maximize the volume of the smallest of them. It is possible to cut the chocolate bar only at the junction of the lobules, and each incision must pass through the entire chocolate bar along some hyperplane involved in the formation of lobules. Only after making all the cuts, Vasya disassembles the chocolate into pieces. More formally, Vasya wants to choose the numbers b_1, b_2, ... , b_n ( 1 <= b_i <= a_i ) -- the number of parts into which Vasya will cut the chocolate bar along each dimension. The condition b_1 cdot b_2 cdot ldots cdot b_n ge k must be met to get at least k pieces after all cuts. It can be noted that with optimal cutting with such parameters, the minimum piece will contain lfloor frac{a_1}{b_1} rfloor ... m lfloor frac{a_n}{b_n} rfloor slices, and its volume will be equal to lfloor frac{a_1}{b_1} rfloor ... m lfloor frac{a_n}{b_n} rfloor cdot frac{1}{a_1 a_2 cdots a_n} . Vasya wants to get the maximum possible value of the volume of the minimum piece multiplied by k , that is, he wants to maximize the number of lfloor frac{a_1}{b_1} rfloor ... m lfloor frac{a_n}{b_n} rfloor cdot frac{1}{a_1 a_2 cdots a_n} cdot k . Help him with this. The first line contains two integers n and k (1 <= n <= 100 , 1 <= k <= 10^7) -- the dimension of the chocolate bar, and how many parts it needs to be divided into. The second line contains n integers a_1, a_2, ... , a_n (1 <= a_i <= 10^7) -- the number of pieces on which the chocolate is placed along each of the dimensions. Print one number -- the maximum possible volume of the smallest of the obtained pieces, multiplied by k , with an absolute or relative error of no more than 10^{-9} . If it is impossible to cut a chocolate bar into at least k pieces u