Hotels Along the Croatian Coast

Along the beautiful Adriatic coast, there are $n$ hotels. Each hotel has its cost in euros. Petr won $m$ euros in the lottery. Now he wants to buy a sequence of consecutive hotels one after another so that the sum of the costs of these consecutive hotels is as large as possible, but does not exceed $m$.

You need to calculate this maximum possible total cost.

Input

The first line contains two integers $n$ and $m(1\le n\le 3\cdot 10^5,1\le m<2^{31})$. The next line contains $n$ positive integers less than $10^6$, representing the costs of the hotels in the order they are located along the coast.

Output

Print the desired maximum cost (it will be greater than $0$ in all tests).

Examples