VECTAR1 - Matrices with XOR property
Imagine A is a NxM matrix with two basic properties
1) Each element in the matrix is distinct and lies in the range of 1<=A[i][j]<=(N*M)
2) For any two cells of the matrix, (i1,j1) and (i2,j2), if (i1^j1) > (i2^j2) then A[i1][j1] > A[i2][j2] ,where
1 ≤ i1,i2 ≤ N
1 ≤ j1,j2 ≤ M.
^ is Bitwise XOR
Given N and M , you have to calculatethe total number of matrices of size N x M which have both the properties
First line contains T, the number of test cases. 2*T lines follow with N on the first line and M on the second, representing the number of rows and columns respectively.
Output the total number of such matrices of size N x M. Since, this answer can be large, output it modulo 10^9+7
1 ≤ N,M,T ≤ 1000
The four possible matrices are:
[1 3] | [2 3] | [1 4] | [2 4]
[4 2] | [4 1] | [3 2] | [3 1]
Please keep in mind that this problem and XORRAY have a significant difference outside of constraints. Array indexing in VECTAR1 is in range <1;D> and in XORARRAY <0;D-1> (D standing for W or H). Both problems are of course correctly described, but it's easy to miss.
Good question!Last edit: 2016-09-27 21:24:38
rainy jain :
Getting TLE , expected complexity?