Distinct Boxes

AtCoder

IDwtf19_d

Time2000ms

Memory256MB

Difficulty—

Snuke has $R$ red balls and $B$ blue balls. He distributes them into $K$ boxes, so that no box is empty and no two boxes are identical. Compute the maximum possible value of $K$. Formally speaking, let's number the boxes $1$ through $K$. If Box $i$ contains $r_i$ red balls and $b_i$ blue balls, the following conditions must be satisfied: * For each $i$ ($1 \leq i \leq K$), $r_i > 0$ or $b_i > 0$. * For each $i, j$ ($1 \leq i < j \leq K$), $r_i \neq r_j$ or $b_i \neq b_j$. * $\sum r_i = R$ and $\sum b_i = B$ (no balls can be left outside the boxes). ## Constraints * $1 \leq R, B \leq 10^{9}$ ## Input Input is given from Standard Input in the following format: $R$ $B$ [samples]

Samples

Input #1

8 3

Output #1

5

The following picture shows one possible way to achieve $K = 5$:
![image](https://img.atcoder.jp/wtf19/9ea9530037df204a84029678052ab593.png)

API Response (JSON)

{
  "problem": {
    "name": "Distinct Boxes",
    "description": {
      "content": "Snuke has $R$ red balls and $B$ blue balls. He distributes them into $K$ boxes, so that no box is empty and no two boxes are identical. Compute the maximum possible value of $K$. Formally speaking, le",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "wtf19_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Snuke has $R$ red balls and $B$ blue balls. He distributes them into $K$ boxes, so that no box is empty and no two boxes are identical. Compute the maximum possible value of $K$.\nFormally speaking, le...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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