A box of pre-cooked food contains N dishes and each dish has 2 properties, its Protein content and its Fat content. We need to select a non-empty subset of these N dishes such that the ratio of total Protein content to total Fat content in these selected subset of dishes is equal to a given target T.

Answer Yes if possible, No otherwise.

Constraints: 1<=N<=50 1<=T,Protein_i,Fat_i<=10

Eg1:

N=3,T=5

[[8,1],[1,1],[2,1]] where first index corresponds to protein content and second is fat content. Answer is "Yes" because selecting 1st and 3rd dish yields (8+2)/(1+1) = 5.

Eg2:

N=3,T=6

[[8,1],[1,1],[2,1]]. Answer is "No"

I don't think bitmask would work given that N can be upto 50. Any other solutions to this problem?