Doubt on Modular Arithmetic

help
1

printf("%lld\n",((2LL*nCr(n+k+1, k+2))%MOD - n + MOD)%MOD);

I came across answer to an editorial solution which required the use of modular arithmetic. My solution could not pass some of the test cases because of the absence of + MOD in the above code. Could someone explain me what normalization does using + MOD bring. Which rule of modular arithmetic is being followed?

2

It might be because the value in your expression give negative values, and mod of that would give wrong answer, So adding mod makes the answer in the range of [0…mod] and correct as well.