Tax Included Price

AtCoder

IDarc118_a

Time2000ms

Memory256MB

Difficulty—

The consumption tax rate in the Republic of ARC is $t$ percent, where $t$ is a positive integer. There is a shop called Seisu-ya _(integer shop)_ there. It sells each positive integer $A$ for $A$ yen (Japanese currency) excluding tax, that is, $\left\lfloor\frac{100+t}{100}A\right\rfloor$ yen including tax. Here, $\lfloor x\rfloor$ denotes the largest integer not greater than $x$ for a real number $x$. Although Seisu-ya sells every positive integer, there are some positive integer values that cannot be the tax-included price of an integer. Among those values, find the $N$\-th smallest value. ## Constraints * $1\leq t\leq 50$ * $1\leq N\leq 10^{9}$ ## Input Input is given from Standard Input in the following format: $t$ $N$ [samples]

Samples

Input #1

10 1

Output #1

10

In this sample, the consumption tax rate is $10$ percent.

*   The integer $9$ is sold for $\left\lfloor \frac{110}{100}\times 9\right\rfloor = \lfloor 9.9\rfloor = 9$ yen including tax.
*   The integer $10$ is sold for $\left\lfloor \frac{110}{100}\times 10\right\rfloor = \lfloor 11\rfloor = 11$ yen including tax.

From above, we can see that $10$ is not the tax-included price of any integer, and this is the minimum such value.

Input #2

3 5

Output #2

171

If the consumption tax rate is $3$ percent, the smallest values that cannot be the tax-included price of an integer are $34, 68, 102, 137, 171, \ldots$

Input #3

1 1000000000

Output #3

100999999999

API Response (JSON)

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    "name": "Tax Included Price",
    "description": {
      "content": "The consumption tax rate in the Republic of ARC is $t$ percent, where $t$ is a positive integer. There is a shop called Seisu-ya _(integer shop)_ there. It sells each positive integer $A$ for $A$ yen ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc118_a"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "The consumption tax rate in the Republic of ARC is $t$ percent, where $t$ is a positive integer.\nThere is a shop called Seisu-ya _(integer shop)_ there. It sells each positive integer $A$ for $A$ yen ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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