G. A Stroll Around the Matrixtime limit per test6 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard output  William has two arrays of numbers a_1, a_2, \dots, a_n and b_1, b_2, \dots, b_m. The arrays satisfy the conditions of being convex. Formally an array c of length k is considered convex if c_i - c_{i - 1} < c_{i + 1} - c_i for all i from 2 to k - 1 and c_1 < c_2.Throughout William's life he observed q changes of two types happening to the arrays:   Add the arithmetic progression d, d \cdot 2, d \cdot 3, \dots, d \cdot k to the suffix of the array a of length k. The array after the change looks like this: [a_1, a_2, \dots, a_{n - k}, a_{n - k + 1} + d, a_{n - k + 2} + d \cdot 2, \dots, a_n + d \cdot k].  The same operation, but for array b. After each change a matrix d is created from arrays a and b, of size n \times m, where d_{i, j}=a_i + b_j. William wants to get from cell (1, 1) to cell (n, m) of this matrix. From cell (x, y) he can only move to cells (x + 1, y) and (x, y + 1). The length of a path is calculated as the sum of numbers in cells visited by William, including the first and the last cells.After each change William wants you to help find out the minimal length of the path he could take.InputThe first line contains three integers n, m and q (2 \le n \le 100, 2 \le m \le 10^5, 1 \le q \le 10^5), the sizes of the arrays and the number of changes.The second line contains n integers a_1, a_2, \dots, a_n (1 \le a_i \le 10^{12}), the contents of array a.The third line contains m integers b_1, b_2, \dots, b_m (1 \le b_i \le 10^{12}), the contents of array b.Each of the next q lines contains three integers type, k and d (1 \le type \le 2, if type = 1, then 1 \le k \le n otherwise 1 \le k \le m, 1 \le d \le 10^3).OutputAfter each change, output one integer, the minimum length of the path in the constructed matrix.ExamplesInput
5 3 4
1 2 4 7 11
5 7 10
1 3 2
2 2 5
1 5 4
2 1 7
Output
98
128
219
229
Input
5 6 7
4 9 22 118 226
7 94 238 395 565 738
2 1 95
1 4 54
1 2 5
1 2 87
2 6 62
2 1 143
1 1 77
Output
3639
5122
5162
5617
7663
7806
7960

5 3 4
1 2 4 7 11
5 7 10
1 3 2
2 2 5
1 5 4
2 1 7

98 128 219 229 
['data structures', 'greedy', 'math', '*3000']