题目描述

People in Silverland use coins.They have coins of value A1​,A2​,A3​...An​ Silverland dollar.One day Tony opened his money-box and found there were some coins.He decided to buy a very nice watch in a nearby shop. He wanted to pay the exact price(without change) and he known the price would not more than m.But he didn't know the exact price of the watch.
You are to write a program which readsn,m,A1​,A2​,A3​...An​andC1​,C2​,C3​...Cn​corresponding to the number of Tony's coins of valueA1​,A2​,A3​...An​ then calculate how many prices(form 1 to m) Tony can pay use these coins.

输入格式

The input contains several test cases. The first line of each test case contains two integers n(1≤n≤100),m(m≤100000).The second line contains 2n integers, denoting A1​,A2​,A3​...An​,C1​,C2​,C3​...Cn​

输出格式

For each test case output the answer on a single line.

样例

3 10
1 2 4 2 1 1
2 5
1 4 2 1
0 0

8
4