#jag2018summerday2k. [jag2018summer_day2_k]Short LIS

[jag2018summer_day2_k]Short LIS

Problem Statement

You are given three integers NN, AA, and BB.

Let P=(P0,P1,...,PN1)P=(P_0,P_1,...,P_{N-1}) be a permutation of (0,1,...,N1)(0,1,...,N-1). PP is said good if and only if it satisfies all of the following conditions:

  • The length of a longest increasing subsequence of PP is at most 22.
  • PA=BP_A = B

Count the number of good permutations modulo 109+710^9+7.

Constraints

  • 1leqNleq1061 \\leq N \\leq 10^6
  • 0leqAleqN10 \\leq A \\leq N-1
  • 0leqBleqN10 \\leq B \\leq N-1

Input

Input is given from Standard Input in the following format:

NN AA BB

Output

Print the number of good permutations modulo 109+710^9+7.


Sample Input 1

3 0 0

Sample Output 1

The only good permutation is (0,2,1)(0,2,1).


Sample Input 2

12 2 3

Sample Output 2

5390

Sample Input 3

10000 9875 5431

Sample Output 3

135608808