The task is adapted from HDOJ 6701 - Make Rounddog Happy.
Bobo has a sequence of integers a1,a2,…,an and an integer m.
Let f(j) be the number of i where 1≤i≤j and max hold. Find the value of f(1), \dots, f(n).
Input
The input consists of several test cases terminated by end-of-file.
The first line of each test case contains two integers n and m, and the second line contains n integers a_1, a_2, \dots, a_n.
- 1 \leq n \leq 10^6
- -n \leq m \leq n
- 1 \leq a_i \leq n
- The sum of n does not exceed 5 \times 10^6.
Output
For each test case, print n integers f(1), \dots, f(n).
Sample Input
3 0 1 3 2 3 1 1 3 2 5 2 1 2 3 4 5
Sample Output
1 2 3 0 2 2 0 0 1 2 3