Hi guys , i'm solving this problem:

For array a[i] with n elements ( 1 <= n <= 3000 , abs(a[i]) <= 10^9 )

Ask: After m loop ( 1 <= m <= 10^9 ) , print all of value in array a. Every loop , a[i]=a[i] + a[i-1] + ... + a[1]

Test input: 5 4 2 8 1 1 2

Test output: 4 10 24 39 55

Explain: loop1: 4 6 14 15 16 loop2: 4 10 24 39 55

My ideas was found formula math

I detects this:

For ex with n=5 , m=5 , in array a[5] , we have: loop1: a5 + a4 + a3 + a2 + a1

loop2: a5 + 2a4 + 3a3 + 4a2 + 5a1

loop3: a5 + 3a4 + 6a3 + 10a2 + 15a1

loop4: a5 + 4a4 + 10a3 + 20a2 + 35a1

loop5: a5 + 5a4 + 15a3 + 35a2 + 70a1

Look at this matrix , we are only care about the coefficent , so we have:

1 1 1 1 1

1 2 3 4 5

1 3 6 10 15

1 4 10 20 35

1 5 15 35 70

So the intiall problem change to the problem how to calcute quickly for function f(i)(j) , with:

f(1)(j) = 1 , f(i)(1) = 1

f(i)(j) = f(i-1)(j) + f(i)(j-1)

I can't find the formular for this function , so i need anybody helps me to find the formular or solve the intiall problem.

Thank you so much !