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/*

Task : Pascal_Triangle

Author : Phumipat C. [MAGCARI]

Language : C++

Explanation :

Created : 22 August 2021 [11:26]

*/

#include<bits/stdc++.h>

#define all(x) begin(x),end(x)

#define sz(x) (int)(x).size()

#define MOD (LL )(1e9+7)

using namespace std;

using LL = long long;

using PII = pair<int ,int >;

using PLL = pair<long long ,long long >;

const int dir4[2][4] = {{1,-1,0,0},{0,0,1,-1}};

const int dir8[2][8] = {{-1,-1,-1,0,1,1,1,0},{-1,0,1,1,-1,0,1,-1}};

const int N = 1010;

int nCr[N][N]; //nCr[i][j] means n = i, r = j [iCj]

void init_triangle(int n){

for(int i=0;i<=n;i++){

nCr[i][0] = nCr[i][i] = 1;

for(int j=1;j<i;j++)

nCr[i][j] = nCr[i-1][j-1] + nCr[i-1][j];

}

}