Task Ordering with Prerequisites

You are given t tasks numbered from 1 to t and p prerequisite pairs. Each prerequisite is given as a pair of integers (a, b), which indicates that task a must be completed before task b can be started.

Your task is to determine a valid order in which all tasks can be performed. Formally, find a sequence \(\pi = [\pi_1, \pi_2, \dots, \pi_t]\) such that for every prerequisite pair \((a, b)\), task a appears before task b in \(\pi\). If no such ordering exists (i.e. the dependency graph contains a cycle), output "IMPOSSIBLE".

inputFormat

The first line contains two integers t and p (\(1 \le t \le 10^5\), \(0 \le p \le 10^5\)), where t is the number of tasks and p is the number of prerequisites.

Each of the next p lines contains two integers a and b (\(1 \le a, b \le t\)), representing a prerequisite: task a must be completed before task b.

outputFormat

If a valid ordering exists, output the task labels in a valid order, separated by a single space.

If it is impossible to complete all tasks due to a cycle in the prerequisites, output "IMPOSSIBLE".

## sample

3 0

1 2 3

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