scheduling exclusive, uniform length, interval constrained events

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n one-day long events are to take place over m days. Each event has a simple date range r1-r2, such that 0 < r1 and r2 <= m, in which it can be scheduled to take place.

Determine whether it's possible to schedule each event exclusively on its own day.

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This is a cumulative constraint with $p_i=c_i=1$ for all $i$ and $C=1$.