#D12374. Martian Dollar
Martian Dollar
Martian Dollar
One day Vasya got hold of information on the Martian dollar course in bourles for the next n days. The buying prices and the selling prices for one dollar on day i are the same and are equal to ai. Vasya has b bourles. He can buy a certain number of dollars and then sell it no more than once in n days. According to Martian laws, one can buy only an integer number of dollars. Which maximal sum of money in bourles can Vasya get by the end of day n?
Input
The first line contains two integers n and b (1 ≤ n, b ≤ 2000) — the number of days and the initial number of money in bourles. The next line contains n integers ai (1 ≤ ai ≤ 2000) — the prices of Martian dollars.
Output
Print the single number — which maximal sum of money in bourles can Vasya get by the end of day n.
Examples
Input
2 4 3 7
Output
8
Input
4 10 4 3 2 1
Output
10
Input
4 10 4 2 3 1
Output
15
inputFormat
Input
The first line contains two integers n and b (1 ≤ n, b ≤ 2000) — the number of days and the initial number of money in bourles. The next line contains n integers ai (1 ≤ ai ≤ 2000) — the prices of Martian dollars.
outputFormat
Output
Print the single number — which maximal sum of money in bourles can Vasya get by the end of day n.
Examples
Input
2 4 3 7
Output
8
Input
4 10 4 3 2 1
Output
10
Input
4 10 4 2 3 1
Output
15
样例
2 4
3 7
8