Find ways to arrange K green balls among N balls such that exactly i moves is needed to collect all K green balls | C ++ implementation of the approach ; To store the factorial and the factorial mod inverse of a number ; Function to find ( a ^ m1 ) % mod ; Function to find factorial of all the numbers ; Function to find the factorial mod inverse of all the numbers ; Function to return nCr ; Function to find ways to arrange K green balls among N balls such that we need exactly i moves to collect all K green balls ; Driver code ; Function call
#include <bits/stdc++.h> NEW_LINE using namespace std ; #define N  100005 NEW_LINE #define mod  (int)(1e9 + 7) NEW_LINE int factorial [ N ] , modinverse [ N ] ; int power ( int a , int m1 ) { if ( m1 == 0 ) return 1 ; else if ( m1 == 1 ) return a ; else if ( m1 == 2 ) return ( 1LL * a * a ) % mod ; else if ( m1 & 1 ) return ( 1LL * a * power ( power ( a , m1 / 2 ) , 2 ) ) % mod ; else return power ( power ( a , m1 / 2 ) , 2 ) % mod ; } void factorialfun ( ) { factorial [ 0 ] = 1 ; for ( int i = 1 ; i < N ; i ++ ) factorial [ i ] = ( 1LL * factorial [ i - 1 ] * i ) % mod ; } void modinversefun ( ) { modinverse [ N - 1 ] = power ( factorial [ N - 1 ] , mod - 2 ) % mod ; for ( int i = N - 2 ; i >= 0 ; i -- ) modinverse [ i ] = ( 1LL * modinverse [ i + 1 ] * ( i + 1 ) ) % mod ; } int binomial ( int n , int r ) { if ( r > n ) return 0 ; int a = ( 1LL * factorial [ n ] * modinverse [ n - r ] ) % mod ; a = ( 1LL * a * modinverse [ r ] ) % mod ; return a ; } void arrange_balls ( int n , int k ) { factorialfun ( ) ; modinversefun ( ) ; for ( int i = 1 ; i <= k ; i ++ ) cout << ( 1LL * binomial ( n - k + 1 , i ) * binomial ( k - 1 , i - 1 ) ) % mod << " ▁ " ; } int main ( ) { int n = 5 , k = 3 ; arrange_balls ( n , k ) ; return 0 ; }