E. Combinatorics Problemtime limit per test4 secondsmemory limit per test1024 megabytesinputstandard inputoutputstandard outputRecall that the binomial coefficient \binom{x}{y} is calculated as follows (x and y are non-negative integers):  if x < y, then \binom{x}{y} = 0;  otherwise, \binom{x}{y} = \frac{x!}{y! \cdot (x-y)!}. You are given an array a_1, a_2, \dots, a_n and an integer k. You have to calculate a new array b_1, b_2, \dots, b_n, where  b_1 = (\binom{1}{k} \cdot a_1) \bmod 998244353;  b_2 = (\binom{2}{k} \cdot a_1 + \binom{1}{k} \cdot a_2) \bmod 998244353;  b_3 = (\binom{3}{k} \cdot a_1 + \binom{2}{k} \cdot a_2 + \binom{1}{k} \cdot a_3) \bmod 998244353, and so on. Formally, b_i = (\sum\limits_{j=1}^{i} \binom{i - j + 1}{k} \cdot a_j) \bmod 998244353.Note that the array is given in a modified way, and you have to output it in a modified way as well.InputThe only line of the input contains six integers n, a_1, x, y, m and k (1 \le n \le 10^7; 0 \le a_1, x, y < m; 2 \le m \le 998244353; 1 \le k \le 5).The array [a_1, a_2, \dots, a_n] is generated as follows:  a_1 is given in the input;  for 2 \le i \le n, a_i = (a_{i-1} \cdot x + y) \bmod m. OutputSince outputting up to 10^7 integers might be too slow, you have to do the following:Let c_i = b_i \cdot i (without taking modulo 998244353 after the multiplication). Print the integer c_1 \oplus c_2 \oplus \dots \oplus c_n, where \oplus denotes the bitwise XOR operator.ExampleInput
5 8 2 3 100 2
Output
1283

5 8 2 3 100 2

1283 
['brute force', 'combinatorics', 'dp', '*2200']