CF1103B Game with modulo


This is an interactive problem.

Vasya and Petya are going to play the following game: Petya has some positive integer number \(a\). After that Vasya should guess this number using the following questions. He can say a pair of non-negative integer numbers \((x,y)\). Petya will answer him:

  • "x", if \((x \bmod a)≥(y \bmod a)\).
  • "y", if \((x \bmod a)<(y \bmod a)\).

We define \((x \bmod a)\) as a remainder of division \(x\) by \(a\).

Vasya should guess the number \(a\) using no more, than 60 questions.

It's guaranteed that Petya has a number, that satisfies the inequality \(1≤a≤10^9\).

Help Vasya playing this game and write a program, that will guess the number \(a\).