G. Recursive Queriestime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a permutation p_1, p_2, \dots, p_n. You should answer q queries. Each query is a pair (l_i, r_i), and you should calculate f(l_i, r_i).Let's denote m_{l, r} as the position of the maximum in subsegment p_l, p_{l+1}, \dots, p_r.Then f(l, r) = (r - l + 1) + f(l, m_{l,r} - 1) + f(m_{l,r} + 1, r) if l \le r or 0 otherwise.InputThe first line contains two integers n and q (1 \le n \le 10^6, 1 \le q \le 10^6) — the size of the permutation p and the number of queries.The second line contains n pairwise distinct integers p_1, p_2, \dots, p_n (1 \le p_i \le n, p_i \neq p_j for i \neq j) — permutation p.The third line contains q integers l_1, l_2, \dots, l_q — the first parts of the queries.The fourth line contains q integers r_1, r_2, \dots, r_q — the second parts of the queries.It's guaranteed that 1 \le l_i \le r_i \le n for all queries.OutputPrint q integers — the values f(l_i, r_i) for the corresponding queries.ExampleInput
4 5
3 1 4 2
2 1 1 2 1
2 3 4 4 1
Output
1 6 8 5 1 
NoteDescription of the queries:   f(2, 2) = (2 - 2 + 1) + f(2, 1) + f(3, 2) = 1 + 0 + 0 = 1;  f(1, 3) = (3 - 1 + 1) + f(1, 2) + f(4, 3) = 3 + (2 - 1 + 1) + f(1, 0) + f(2, 2) = 3 + 2 + (2 - 2 + 1) = 6;  f(1, 4) = (4 - 1 + 1) + f(1, 2) + f(4, 4) = 4 + 3 + 1 = 8;  f(2, 4) = (4 - 2 + 1) + f(2, 2) + f(4, 4) = 3 + 1 + 1 = 5;  f(1, 1) = (1 - 1 + 1) + 0 + 0 = 1. 
4 5
3 1 4 2
2 1 1 2 1
2 3 4 4 1

1 6 8 5 1  
['data structures', '*2500']