Splitting into Combination Numbers

Given two integers \(x\) and \(k\), split \(x\) into exactly \(k\) distinct combination numbers in the form \(C(n, m)\). Two combination numbers \(C(n_1, m_1)\) and \(C(n_2, m_2)\) are considered different if \(n_1 \neq n_2\) or \(m_1 \neq m_2\). Moreover, every combination number chosen must satisfy \(0 \le m \le n \le x\). The value of a combination number is defined in the standard way as \(C(n, m)=\binom{n}{m}\). It is guaranteed that a solution exists.

Your task is to output exactly \(k\) lines, each containing two space-separated integers \(n\) and \(m\) representing a combination number \(C(n, m)\), such that the sum of all combination numbers equals \(x\).

inputFormat

The input consists of two integers \(x\) and \(k\) separated by a space.

outputFormat

Output \(k\) lines. Each line should contain two integers \(n\) and \(m\), separated by a space, representing a combination number \(C(n, m)\). The sum of all the combination numbers must equal \(x\).

sample

10 3

8 1
0 0
1 0