P402663 - GYM100834 L Polycarp and Permutations - SSOJ

Memory Limit：512 MB Time Limit：3 S

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L. Polycarp and Permutationstime limit per test3 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard output

Polycarp has set of integers 1, ..., N and parameters M и K. Polycarp is interested in number of permutations {a_i} from numbers 1, ..., N, so that every permutation have exactly M inversions and K numbers are in their own place. Inversion is the pair of numbers i, j, so that a_i > a_j и i < j. Number i is postioned in it's own place if a_i = i.

Input

Single line contains three integers N, M, K. 1 ≤ N ≤ 14, $\text{[math]}$ , 0 ≤ K ≤ N.

Output

One integer — number or permutations.

ExamplesInput

4 0 4

Output

Input

12 7 3

Output

Input

12 25 0

Output

Input

12 66 0

Output

VIII Open Programming Championship of Kazan Federal University 2015

402663: GYM100834 L Polycarp and Permutations

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