# 1494. Coins

People in Silverland use coins. They have coins of value $A_1,A_2,A_3,\ldots,A_n$ 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 reads $n,m,A_1,A_2,A_3,\ldots,A_n$ and $C_1,C_2,C_3,\ldots,C_n$ corresponding to the number of Tony’s coins of value $A_1,A_2,A_3,\ldots,A_n$ then calculate how many prices (from $1$ to $m$) Tony can pay use these coins.

### 输入格式

The first line of test case contains two integers $n$ $(1 \le n \le 100)$, $m$ $(m \le 100~000)$. The second line contains $2n$ integers, denoting $A_1,A_2,A_3,\ldots,A_n,C_1,C_2,C_3,\ldots,C_n$ $(1 \le A_i \le 100~000, 1 \le Ci \le 1000)$.

### 输出格式

Output the answer on a single line.

### 样例

Input
2 5
1 4 2 1

Output
4


42 人解决，54 人已尝试。

59 份提交通过，共有 166 份提交。

4.1 EMB 奖励。