A company has N API endpoints. Activating the i-th endpoint requires bandwidth[i] units of bandwidth and allows it to serve request[i] requests.

You have a total of B units of bandwidth.

Choose a subset of endpoints such that the total bandwidth used does not exceed B, while maximizing the total number of requests served.

Print the maximum possible number of requests.

Input Format The first line contains two integers N and B. The second line contains N integers bandwidth[i]. The third line contains N integers request[i]. Output Format

Print a single integer — the maximum number of requests that can be served.