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B. Cells Not Under Attack

time limit per test2 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output
Vasya has the square chessboard of size n × n and m rooks. Initially the chessboard is empty. Vasya will consequently put the rooks on the board one after another.

The cell of the field is under rook’s attack, if there is at least one rook located in the same row or in the same column with this cell. If there is a rook located in the cell, this cell is also under attack.

You are given the positions of the board where Vasya will put rooks. For each rook you have to determine the number of cells which are not under attack after Vasya puts it on the board.

Input
The first line of the input contains two integers n and m (1 ≤ n ≤ 100 000, 1 ≤ m ≤ min(100 000, n2)) — the size of the board and the number of rooks.

Each of the next m lines contains integers xi and yi (1 ≤ xi, yi ≤ n) — the number of the row and the number of the column where Vasya will put the i-th rook. Vasya puts rooks on the board in the order they appear in the input. It is guaranteed that any cell will contain no more than one rook.

Output
Print m integer, the i-th of them should be equal to the number of cells that are not under attack after first i rooks are put.

Examples
input
3 3
1 1
3 1
2 2
output
4 2 0
input
5 2
1 5
5 1
output
16 9
input
100000 1
300 400
output
9999800001
Note
On the picture below show the state of the board after put each of the three rooks. The cells which painted with grey color is not under the attack.

Codeforces (c) Copyright 2010-2016 Mike Mirzayanov
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include”iostream”

using namespace std;
typedef long long ll;
int visitx[1000050];
int visity[1000050];
int main()
{
//freopen(“a.txt”,”r”,stdin);
ll n,k;
while(scanf(“%I64d%I64d”,&n,&k)!=EOF)
{
memset(visitx,0,sizeof(visitx));
memset(visity,0,sizeof(visity));
ll a,b;
a=b=0;
int first=1;
for(int i=0;i