Problem Statement

The mixed juice has run out.
The ingredient label of the mixed juice lists, in order, fruit \(1\), fruit \(2\), \(\ldots\), fruit \(N\).
You want to make exactly \(V\) liters of mixed juice by mixing the existing 100% juices of each fruit.
The 100% juice of fruit \(k\) is sold only in \(1\)-liter packs, at \(C_k\) yen per \(1\) pack.
Write a program that finds the minimum cost of making \(V\) liters of mixed juice without changing the ingredient label.
That is, the proportions \(p_k\) that fruit \(k\) occupies in the mixed juice must satisfy \(p_1 \geq p_2 \geq \cdots \geq p_N\), and furthermore, no fruit may be left unused.
It is also possible to buy a \(1\)-liter pack and use only part of it.

Input

\(N\) \(V\)
\(C_1\) \(C_2\) ... \(C_N\)

Line \(1\) contains an integer \(N\ (1 \leq N \leq 100)\) representing the number of kinds of fruit and an integer \(V\ (1 \leq V \leq 10^9)\) representing the amount of mixed juice you want to make.
Line \(2\) contains, in order and separated by spaces, integers \(C_k\ (1 \leq C_k \leq 10^9)\) representing the price of a \(1\)-liter pack of the 100% juice of fruit \(k\).

Output

Output an integer representing the minimum cost (in yen) on \(1\) line. Print a newline at the end.

Sample

3 10
1 100 100

208

3 10
100 1 100

604

3 10
100 100 1

703

3 1
100 100 100

300

9 36
459473288 389234620 200824516 103210888 47314058 533584454 391380554 875989889 257188584

10107195609