Read matrix A (r × k) and matrix B (p × c). If they cannot be multiplied (k ≠ p), print INVALID. Otherwise print the r × c product, one row per line.
Use long[][] arrays in Java.
Constraints
- 1 ≤ r, k, p, c ≤ 100
- −1000 ≤ entries ≤ 1000
Input and output
- Input
- Line: r k, then r lines of A. Line: p c, then p lines of B.
- Output
- The product matrix, or `INVALID`.
Examples
Input 1
2 3
1 2 3
4 5 6
3 2
7 8
9 10
11 12Output
58 64
139 154Row 1: 1·7 + 2·9 + 3·11 = 58 and 1·8 + 2·10 + 3·12 = 64.
Input 2
1 2
1 2
3 1
1
2
3Output
INVALIDA has 2 columns but B has 3 rows, so INVALID.
Show hints
- C[i][j] is the dot product of row i of A and column j of B.
- Looping i, t, j (instead of i, j, t) reads memory in row order and is faster.
Show the explanation
The product exists only when A's column count equals B's row count. Then C[i][j] = Σ A[i][t] · B[t][j] over t. Three nested loops give O(r · k · c). Ordering the loops i → t → j lets the inner loop walk rows of B and C contiguously, which is friendlier to the CPU cache than i → j → t. Use long because sums of products can exceed int.
Original UniCircle question. Last reviewed 22 Oct 2026.