B'Farmer John has an array a of length n . He also has a function f with the following recurrence: Note that f(i) is not necessarily an integer. He plans to do q updates to the array. Each update, he gives you two integers k and x and he wants you to set a_k = x . After each update, he wants to know lfloor f(n) rfloor , where lfloor t rfloor denotes the value of t rounded down to the nearest integer. The first line contains n and q ( 1 <= q n, q <= q 2 cdot 10^5 ), the length of a and the number of updates he will perform. The second line contains n integers a_1, a_2, ldots, a_n ( 0 <= q a_i <= q 10^{18} ). The next q lines each contain two integers k and x ( 1 <= q k <= q n , 0 <= q x <= q 10^{18} ), the index of the update and the element he will replace a_k with. For each update, output an integer, lfloor f(n) rfloor , on a new line. In the first test case, the array after the first update is [4, 14, 0, 7, 6] . The values of f are: Since lfloor f(5) rfloor = 3 , we output 3 . The array after the second update is [3, 14, 0, 7, 6] . The values of f , rounded to 6 decimal places, are: Since lfloor f(5) rfloor = 2 , we output 2 . '...