Binary Scale

A binary scale is a special device that can measure any value in the open interval $(0, 1)$ with a fixed precision. The precision is set with a dial that can be turned to $1, 2, 3, \dots, 10$. When the precision is set to $m$, the scale measures in units of $1 / 2^m$.

A measurement is recorded as a pair $(\ell, m)$. Such a pair means the precision is set to $m$ and the scale reads $\ell$, so the weight of the measured object is $\ell / 2^m$. Here $\ell$ is a positive integer, and since the scale only reads values in $(0, 1)$ we have $0 < \ell < 2^m$.

Write a program that orders the measurements from the smallest value to the largest. Each measurement is given as a pair $(\ell, m)$. Different pairs that represent the same value (for example $(1, 2)$ and $(2, 3)$, both equal to $1/4$) must be ordered by increasing reading $\ell$, the first element of the pair.

The program reads from standard input. The first line contains an integer $n$ ($1 \le n \le 20\,000$), the number of pairs. Each of the next $n$ lines contains one pair $\ell_i$ and $m_i$, separated by a single space. For every pair, $1 \le m_i \le 10$ and $1 \le \ell_i < 2^{m_i}$.

The program writes to standard output. Output the $n$ input pairs, reordered so that pairs with smaller measured values come before pairs with larger measured values. Pairs with equal measured values are printed in non-decreasing order of their reading $\ell$. Print each pair in the same format as the input, that is, the two integers $\ell_i$ and $m_i$ separated by a single space.