102314: [AtCoder]ABC231 E - Minimal payments

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

Score : $500$ points

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

Input

题意翻译

现有 $n$ 种硬币。 每个硬币的面额为 $A_1,A_2,...,A_n$ 。 现在,你想买价值为 $x$ 元钱的物品。 求你用出的硬币个数和商家找回的硬币个数的总和的最小值是多少。

Output

分数:500分

问题描述

在Atcoder王国中,有N种硬币:A1日元硬币,A2日元硬币,...,AN日元硬币。

这里,1=A1 < ... < AN成立,并且对于每一个1≤i≤N-1,Ai+1是Ai的倍数。

当使用这些硬币支付价值为X日元的商品时,支付和找零所需的硬币总数的最小值是多少?

准确地说,当Y是至少为X的整数时,找出表示Y日元所需的硬币数量和表示Y-X日元所需的硬币数量的最小和。

约束条件

  • 输入中的所有值都是整数。
  • 1≤N≤60
  • 1=A1 < ... < AN≤1018
  • 对于每一个1≤i≤N-1,Ai+1是Ai的倍数。
  • 1≤X≤1018

输入

输入将以标准输入的以下格式给出:

$N$ $X$
$A_1$ $\ldots$ $A_N$

输出

打印答案。


样例输入1

3 87
1 10 100

样例输出1

5

如果我们支付一个100日元硬币并收到一个10日元硬币和三个1日元硬币作为找零,硬币的总数量将是5。


样例输入2

2 49
1 7

样例输出2

7

使用七个7日元硬币支付是最佳选择。


样例输入3

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

样例输出3

233

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