Score : $500$ points

问题描述

在Atcoder王国中，有$N$种硬币：$A_1$日元、$A_2$日元、$\ldots$、$A_N$日元硬币。 这里满足条件 $1=A_1 < \ldots < A_N$，并且对于任意的 $1\leq i \leq N-1$，都有 $A_{i+1}$ 是 $A_i$ 的倍数。

当仅使用这些硬币支付价值为 $X$ 日元的商品时，付款及找零所需的最小总硬币数量是多少？

准确地说，当 $Y$ 是大于等于 $X$ 的整数时，求表示正好 $Y$ 日元所需硬币数量与表示正好 $Y-X$ 日元所需硬币数量之和的最小值。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

There are $N$ kinds of coins used in the Kingdom of Atcoder: $A_1$-yen, $A_2$-yen, $\ldots$, $A_N$-yen coins.
Here, $1=A_1 < \ldots < A_N$ holds, and $A_{i+1}$ is a multiple of $A_i$ for every $1\leq i \leq N-1$.

When paying for a product worth $X$ yen using just these coins, what is the minimum total number of coins used in payment and returned as change?

Accurately, when $Y$ is an integer at least $X$, find the minimum sum of the number of coins needed to represent exactly $Y$ yen and the number of coins needed to represent exactly $Y-X$ yen.

Constraints

• All values in input are integers.
• $1 \leq N \leq 60$
• $1=A_1 < \ldots <A_N \leq 10^{18}$
• $A_{i+1}$ is a multiple of $A_i$ for every $1\leq i \leq N-1$.
• $1\leq X \leq 10^{18}$

Input

Input is given from Standard Input in the following format:

$N$ $X$

$A_1$ $\ldots$ $A_N$

Output

Print the answer.

Sample Input 1

3 87
1 10 100

Sample Output 1

5

If we pay with one $100$-yen coin and receive one $10$-yen coin and three $1$-yen coins as the change, the total number of coins will be $5$.

Sample Input 2

2 49
1 7

Sample Output 2

7

It is optimal to pay with seven $7$-yen coins.

Sample Input 3

10 123456789012345678
1 100 10000 1000000 100000000 10000000000 1000000000000 100000000000000 10000000000000000 1000000000000000000

Sample Output 3

233

update @ 2024/3/10 10:05:01