Evergrowing Tree

AtCoder

IDrelay2_b

Time2000ms

Memory256MB

Difficulty—

You are given an integer $N$. Consider an infinite $N$\-ary tree as shown below: ![image](https://img.atcoder.jp/relay2/c76baa50b0acf28062688597724a54b9.png)Figure: an infinite $N$\-ary tree for the case $N = 3$ As shown in the figure, each vertex is indexed with a unique positive integer, and for every positive integer there is a vertex indexed with it. The root of the tree has the index $1$. For the remaining vertices, vertices in the upper row have smaller indices than those in the lower row. Among the vertices in the same row, a vertex that is more to the left has a smaller index. Regarding this tree, process $Q$ queries. The $i$\-th query is as follows: * Find the index of the lowest common ancestor (see Notes) of Vertex $v_i$ and $w_i$. ## Constraints * $1 ≤ N ≤ 10^9$ * $1 ≤ Q ≤ 10^5$ * $1 ≤ v_i < w_i ≤ 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $Q$ $v_1$ $w_1$ $:$ $v_Q$ $w_Q$ [samples] ## Notes * In a rooted tree, the _lowest common ancestor_ (LCA) of Vertex $v$ and $w$ is the farthest vertex from the root that is an ancestor of both Vertex $v$ and $w$. Here, a vertex is considered to be an ancestor of itself. For example, in the tree shown in Problem Statement, the LCA of Vertex $5$ and $7$ is Vertex $2$, the LCA of Vertex $8$ and $11$ is Vertex $1$, and the LCA of Vertex $3$ and $9$ is Vertex $3$.

Samples

Input #1

Output #1

2
1
3

The queries in this case correspond to the examples shown in Notes.

Input #2

100000 2
1 2
3 4

Output #2

1
1

API Response (JSON)

{
  "problem": {
    "name": "Evergrowing Tree",
    "description": {
      "content": "You are given an integer $N$. Consider an infinite $N$\\-ary tree as shown below: ![image](https://img.atcoder.jp/relay2/c76baa50b0acf28062688597724a54b9.png)Figure: an infinite $N$\\-ary tree for the ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "relay2_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer $N$. Consider an infinite $N$\\-ary tree as shown below:\n\n![image](https://img.atcoder.jp/relay2/c76baa50b0acf28062688597724a54b9.png)Figure: an infinite $N$\\-ary tree for the ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments