F. AND Segmentstime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given three integers n, k, m and m conditions (l_1, r_1, x_1), (l_2, r_2, x_2), \dots, (l_m, r_m, x_m).Calculate the number of distinct arrays a, consisting of n integers such that:   0 \le a_i < 2^k for each 1 \le i \le n;  bitwise AND of numbers a[l_i] \& a[l_i + 1] \& \dots \& a[r_i] = x_i for each 1 \le i \le m. Two arrays a and b are considered different if there exists such a position i that a_i \neq b_i. The number can be pretty large so print it modulo 998244353.InputThe first line contains three integers n, k and m (1 \le n \le 5 \cdot 10^5, 1 \le k \le 30, 0 \le m \le 5 \cdot 10^5) — the length of the array a, the value such that all numbers in a should be smaller than 2^k and the number of conditions, respectively.Each of the next m lines contains the description of a condition l_i, r_i and x_i (1 \le l_i \le r_i \le n, 0 \le x_i < 2^k) — the borders of the condition segment and the required bitwise AND value on it.OutputPrint a single integer — the number of distinct arrays a that satisfy all the above conditions modulo 998244353.ExamplesInput
4 3 2
1 3 3
3 4 6
Output
3
Input
5 2 3
1 3 2
2 5 0
3 3 3
Output
33
NoteYou can recall what is a bitwise AND operation here.In the first example, the answer is the following arrays: [3, 3, 7, 6], [3, 7, 7, 6] and [7, 3, 7, 6].
4 3 2
1 3 3
3 4 6

3 
['bitmasks', 'combinatorics', 'data structures', 'dp', 'two pointers', '*2500']