Problem:
Score : 500 points

Problem Statement

AtCoDeer is thinking of painting an infinite two-dimensional grid in a checked pattern of side K.
Here, a checked pattern of side K is a pattern where each square is painted black or white so that each connected component of each color is a K × K square.
Below is an example of a checked pattern of side 3:

AtCoDeer has N desires.
The i-th desire is represented by x_i, y_i and c_i.
If c_i is B, it means that he wants to paint the square (x_i,y_i) black; if c_i is W, he wants to paint the square (x_i,y_i) white.
At most how many desires can he satisfy at the same time?

Constraints

1 ≤ N ≤ 10^5

1 ≤ K ≤ 1000

0 ≤ x_i ≤ 10^9

0 ≤ y_i ≤ 10^9

If i ≠ j, then (x_i,y_i) ≠ (x_j,y_j).

c_i is B or W.

N, K, x_i and y_i are integers.

Input

Input is given from Standard Input in the following format:

N K
x_1 y_1 c_1
x_2 y_2 c_2
:
x_N y_N c_N

Output

Print the maximum number of desires that can be satisfied at the same time.

Sample Input 1

4 3
0 1 W
1 2 W
5 3 B
5 4 B

Sample Output 1

4

He can satisfy all his desires by painting as shown in the example above.

Sample Input 2

2 1000
0 0 B
0 1 W

Sample Output 2

2

Sample Input 3

6 2
1 2 B
2 1 W
2 2 B
1 0 B
0 6 W
4 5 W

Sample Output 3

4

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
int l,m,s[2010][2010][2],d[2010][2010][2];
int MAX(int a,int b){return a<b?b:a;}
int MIN(int a,int b){return a<b?a:b;}
int f(int a){return MIN(MAX(0,a),l);}
int g(int y,int x,int a){return s[f(y)][f(x)][a]+s[f(y+m)][f(x+m)][a]-s[f(y+m)][f(x)][a]-s[f(y)][f(x+m)][a];}
int main(){
  int n,i,j,k,ans=0,q,x,y;
  char c;
  scanf("%d %d",&n,&m);
  l=m*2;
  while(n--){
    scanf("%d %d %c",&x,&y,&c);
    d[y%l][x%l][c=='W'?0:1]=1;
  }
  for(i=0;i<l;i++){
    for(j=0;j<l;j++){
      for(k=0;k<2;k++)s[i+1][j+1][k]=s[i][j+1][k]+s[i+1][j][k]-s[i][j][k]+d[i][j][k];
    }
  }
  for(i=0;i<l;i++){
    for(j=0;j<l;j++){
      for(k=q=0;k<25;k++){
	q+=g(i+(k/5-2)*m,j+(k%5-2)*m,k%2);
      }
      ans=MAX(ans,q);
    }
  }
  printf("%d\n",ans);
  return 0;
}