CF538H Summer Dichotomy

$ T $ students applied into the ZPP class of Summer Irrelevant School. The organizing committee of the school may enroll any number of them, but at least $ t $ students must be enrolled. The enrolled students should be divided into two groups in any manner (it is possible that one of the groups will be empty!) During a shift the students from the ZPP grade are tutored by $ n $ teachers. Due to the nature of the educational process, each of the teachers should be assigned to exactly one of two groups (it is possible that no teacher will be assigned to some of the groups!). The $ i $ -th teacher is willing to work in a group as long as the group will have at least $ l_{i} $ and at most $ r_{i} $ students (otherwise it would be either too boring or too hard). Besides, some pairs of the teachers don't like each other other and therefore can not work in the same group; in total there are $ m $ pairs of conflicting teachers. You, as the head teacher of Summer Irrelevant School, have got a difficult task: to determine how many students to enroll in each of the groups and in which group each teacher will teach.

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