When Petya has free from computer games time, he attends university classes. Every day the lessons on Petya’s faculty consist of two double classes. The floor where the lessons take place is a long corridor with M classrooms numbered from 1 to M, situated along it.

All the students of Petya’s year are divided into N

 groups. Petya has noticed recently that these groups’ timetable has the following peculiarity: the number of the classroom where the first lesson of a group takes place does not exceed the number of the classroom where the second lesson of this group takes place.

Once Petya decided to count the number of ways in which one can make a lesson timetable for all these groups. The timetable is a set of 2N

 numbers: for each group the number of the rooms where the first and the second lessons take place. Unfortunately, he quickly lost the track of his calculations and decided to count only the timetables that satisfy the following conditions:

1) On the first lesson in classroom i exactly Xi groups must be present.

2) In classroom i no more than Yi groups may be placed.

Help Petya count the number of timetables satisfying all those conditionsю As there can be a lot of such timetables, output modulo 109 + 7.