I realised this problems requires DP, but could not form the recurrence relation. It would be great if any one could explain it a bit.
You can iterate through all the possible values and store the values in 2D matrix say
dp[i][j] means number of ways to reach total sum
N from day number
i and when current sum is
j. My code
It can be done using linear dp as well. You need to construct a dp[N+1] where dp[I] contains the number of ways you can reach the total sum I. You can then iterate over k days and keep updating dp[N+1]. My solution