B. Two Cakes

Codeforces

IDCF911B

Time1000ms

Memory256MB

Difficulty—

binary searchbrute forceimplementation

It's New Year's Eve soon, so Ivan decided it's high time he started setting the table. Ivan has bought two cakes and cut them into pieces: the first cake has been cut into _a_ pieces, and the second one — into _b_ pieces. Ivan knows that there will be _n_ people at the celebration (including himself), so Ivan has set _n_ plates for the cakes. Now he is thinking about how to distribute the cakes between the plates. Ivan wants to do it in such a way that all following conditions are met: 1. Each piece of each cake is put on some plate; 2. Each plate contains at least one piece of cake; 3. No plate contains pieces of both cakes. To make his guests happy, Ivan wants to distribute the cakes in such a way that the minimum number of pieces on the plate is maximized. Formally, Ivan wants to know the maximum possible number _x_ such that he can distribute the cakes according to the aforementioned conditions, and each plate will contain at least _x_ pieces of cake. Help Ivan to calculate this number _x_! ## Input The first line contains three integers _n_, _a_ and _b_ (1 ≤ _a_, _b_ ≤ 100, 2 ≤ _n_ ≤ _a_ + _b_) — the number of plates, the number of pieces of the first cake, and the number of pieces of the second cake, respectively. ## Output Print the maximum possible number _x_ such that Ivan can distribute the cake in such a way that each plate will contain at least _x_ pieces of cake. [samples] ## Note In the first example there is only one way to distribute cakes to plates, all of them will have 1 cake on it. In the second example you can have two plates with 3 and 4 pieces of the first cake and two plates both with 5 pieces of the second cake. Minimal number of pieces is 3.

Samples

Input #1

5 2 3

Output #1

Input #2

4 7 10

Output #2

API Response (JSON)

{
  "problem": {
    "name": "B. Two Cakes",
    "description": {
      "content": "It's New Year's Eve soon, so Ivan decided it's high time he started setting the table. Ivan has bought two cakes and cut them into pieces: the first cake has been cut into _a_ pieces, and the second o",
      "description_type": "Markdown"
    },
    "platform": "Codeforces",
    "limit": {
      "time_limit": 1000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "CF911B"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "It's New Year's Eve soon, so Ivan decided it's high time he started setting the table. Ivan has bought two cakes and cut them into pieces: the first cake has been cut into _a_ pieces, and the second o...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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