Max Subjects Number

In subject i you have already answered answered[i] questions correctly, and you pass once you reach needed[i]. You can answer q more questions correctly in total; find the maximum number of subjects you can pass. Subjects already passed need no extra answers.

输入格式

The first line contains n q, the second line contains answered, and the third line contains needed. 1≤n≤100000, 0≤elements of both arrays≤10^9. On this site 0≤q≤10^14.

输出格式

Output one integer, the answer.

样例 1

输入：

3 100
24 27 0
51 52 100

输出：

2

样例 2

输入：

3 200
24 27 0
51 52 100

输出：

3

样例 3

输入：

2 0
5 0
1 1

输出：

1

样例说明

The examples give 2, 3 and 1 respectively.