SPOJ VECTAR1

大体题意：

问你有多少个矩阵满足(i1,j1) and (i2,j2), if (i1^j1) > (i2^j2) then A[i1][j1] > A[i2][j2]

对1e9+7取模

思路：

当i1^j1 == i2^j2 的时候不能比较大小， 全排列就好了。

因此问题转换为有多少个i1^j1 == i2^j2 的位置，全排列乘起来就好了

#include <cstdio>#include <cstring>#include <algorithm>#include <vector>#define Siz(x) (int)x.size()using namespace std;typedef long long LL;const int mod = 1e9+7;int n,m,T;int vis[2048];LL JIE[2048];void init(){    JIE[0] = 1;    for (int i = 1; i < 2048 ;++i){        JIE[i] = (JIE[i-1] * i) % mod;    }}int main(){    scanf("%d",&T);    init();    while(T--){        scanf("%d %d",&n, &m);        memset(vis,0,sizeof vis);        for (int i = 1; i <= n; ++i){            for (int j = 1; j <= m; ++j){                vis[i^j]++;            }        }        LL ans = 1LL;        for (int i = 0; i < 2048; ++i){            if (vis[i]) ans = (ans*JIE[vis[i]]) % mod;        }        printf("%lld\n",ans);    }    return 0;}

VECTAR1 - Matrices with XOR property

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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.

Given N and M , you have to calculatethe total number of matrices of size N x M which have both the properties

mentioned above.  

Input format:

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 format:

Output the total number of such matrices of size N x M. Since, this answer can be large, output it modulo 10^9+7

Constraints:

1 ≤ N,M,T ≤ 1000

SAMPLE INPUT 

1

2

2

SAMPLE OUTPUT 

4

Explanation

The four possible matrices are:

[1 3] | [2 3] | [1 4] | [2 4]

[4 2] | [4 1] | [3 2] | [3 1]

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

mentioned above.  

Input format:

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 format:

Output the total number of such matrices of size N x M. Since, this answer can be large, output it modulo 10^9+7

Constraints:

1 ≤ N,M,T ≤ 1000

SAMPLE INPUT 

1

2

2

SAMPLE OUTPUT 

4

Explanation

The four possible matrices are:

[1 3] | [2 3] | [1 4] | [2 4]

[4 2] | [4 1] | [3 2] | [3 1]

 

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