Minimal payments

AtCoder

IDabc231_e

Time2000ms

Memory256MB

Difficulty—

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: $N$ $X$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

3 87
1 10 100

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 $5$.

Input #2

2 49
1 7

Output #2

7

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

Input #3

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

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Minimal payments",
    "description": {
      "content": "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",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc231_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ kinds of coins used in the Kingdom of Atcoder: $A_1$\\-yen, $A_2$\\-yen, $\\ldots$, $A_N$\\-yen coins.  \nHere, $1=A_1 < \\ldots < A_N$ holds, and $A_{i+1}$ is a multiple of $A_i$ for every $1...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments