Great great DP learning experience:
http://www.cnblogs.com/yuzhangcmu/p/4279676.html
Remember 2 steps of DP: a) setup state transfer equation; b) setup selection strategy.
a) States
From problem statement, we find 3 variables: array size, k and target. So it is 3D DP:
dp[i][j][t]: in previous i elements, we pick j of them, to reach value t - number of results
b) Selection Strategy
Usually for 1D array, selection strategy is very simple: with A[i] - pick it or not. Combined with step a, dp[i][j][t] is result of the 2 choices - pick or not:
dp[i][j][t] = dp[i-1][j-1][t-A[i]](pick it) + dp[i-1][j][t](no pick)
Optimization: dimension i can be eliminated.
Details: To start: all dp[*][0][0] = 1