402203: GYM100694 M The Fifth Season

Cersei and Jaime has stolen n gold coins from the Casterly Rock reserves. They decided to play a game while the disappearence is not detected.

The game consists of q rounds. At the beginning of each round all n coins lie in a heap. The players move in rotation, taking from the heap no less than k_i and no more than l_i coins (k_i ≤ l_i, i is the number of round). The player who can't do the move loses.

Cersei and Jaime have determined the pairs of numbers (k_i, l_i) for each round of the game. They don't see any point in finding out who wins in what round as they choose who moves the first by flipping a coin. They are interested in the maximal length of each round, provided that they play optimally (intend to win). The length of the round is the total number of moves made by both Cersei and Jaime.

Your task is to find the maximal possible length of each round of the game.

The first line contains two integers n and q — the number of coins and the number of rounds (1 ≤ n ≤ 10⁶, 1 ≤ q ≤ 10⁵).

Each of the next q lines contains two integers k_i and l_i  — the minimal and maximal number of coins that could be taken at one turn in the i-th round.

Write q space-separated integers. The i-th number should be equal to the maximal possible length of the i-th round.

10 2
1 1
5 6

10 1