There are M objects of type 1 and N objects of Type 2. Given Cost[i][j] where i is an object of Type 1, and j is an object of Type 2. What is the minimum total cost achievable after every type 1 object is mapped with exactly one type 2 object?

Total cost is defined as the summation of the individual costs incurred due to matching.

M <= N.

Example : Type 1 : A B

Type 2 : C D

cost[A][C] = 100

cost[A][D] = 10

cost[B][C] = 10

cost[B][D] = 100.

It's optimal to match (A, D) and (B, C), the total cost incurred is 20.

I thought of a bit masking + DP approach, but the complexity is exponential, is there a better approach?