Rectangle update and rectangle sum

You have an $N \times M$ grid. Rows are numbered 1 to $N$ from bottom to top, columns are numbered 1 to $M$ from left to right, and every cell starts at 0. Cell $(i, j)$ is the cell where row $i$ meets column $j$.

Process $Q$ operations on the grid, in the order given.

1 a b x y w: add $w$ to every cell of the rectangle whose bottom left cell is $(a, b)$ and whose top right cell is $(x, y)$.

2 a b x y: print the sum of every cell of the rectangle whose bottom left cell is $(a, b)$ and whose top right cell is $(x, y)$.

The first line holds $N$, $M$, and $Q$, separated by spaces. Each of the next $Q$ lines holds one operation in the format above.

$1 \le N, M \le 1000$ and $1 \le Q \le 100000$. Every operation satisfies $1 \le a \le x \le N$ and $1 \le b \le y \le M$, and $w$ in an operation of type 1 is an integer with $1 \le w \le 1000$.

For each operation of type 2, print the sum on its own line, in input order. A sum can exceed the range of a 32-bit integer.