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USTC has recently developed the Parallel Matrix Multiplication Machine – PM3, which is used for very large matrix multiplication.
Given two matrices A and B, where A is an N × P matrix and B is a P × M matrix, PM3 can compute matrix C = AB in O(P(N + P + M)) time. However the developers of PM3 soon discovered a small problem: there is a small chance that PM3 makes a mistake, and whenever a mistake occurs, the resultant matrix C will contain exactly one incorrect element.
The developers come up with a natural remedy. After PM3 gives the matrix C, they check and correct it. They think it is a simple task, because there will be at most one incorrect element.
So you are to write a program to check and correct the result computed by PM3.
The first line of the input three integers N, P and M (0 < N, P, M ≤ 1,000), which indicate the dimensions of A and B. Then follow N lines with P integers each, giving the elements of A in row-major order. After that the elements of B and C are given in the same manner.
Elements of A and B are bounded by 1,000 in absolute values which those of C are bounded by 2,000,000,000.
If C contains no incorrect element, print “
2 3 2 1 2 -1 3 -1 0 -1 0 0 2 1 3 -2 -1 -3 -2
No 1 2 1
The test set contains large-size input. Iostream objects in C++ or Scanner in Java might lead to efficiency problems.
POJ Monthly--2007.04.01, zhucheng
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