Coins (多重背包)模板题

最新推荐文章于 2025-04-23 12:33:35 发布

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最新推荐文章于 2025-04-23 12:33:35 发布 · 1k 阅读

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本文介绍了一种多重背包问题的模板，涉及硬币支付与找零优化。给定不同面值的硬币及数量，目标是计算能够精确支付1到m范围内多少种价格。输入包括硬币种类数n、最大价格m以及每种硬币的面值和数量。通过将问题分解为完全背包和01背包，利用二进制优化来避免超时，找出能支付的最大价值。

~~模板请看上一篇博客~~

Whuacmers use coins.They have coins of value A1,A2,A3...An Silverland dollar. One day Hibix opened purse 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,A1,A2,A3...An and C1,C2,C3...Cn corresponding to the number of Tony's coins of value A1,A2,A3...An then calculate how many prices(form 1 to m) Tony can pay use these coins.

Input

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 (1 ≤ Ai ≤ 100000,1 ≤ Ci ≤ 1000). The last test case is followed by two zeros.

Output

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