You can think it like this:

If you are at index i and you need x pairs, you have two options: 1) take the sum of the next m elements, move to index i+m and now look for x-1 pairs 2) move to index i+1 and look for x pairs

That can be written as a dp with two states: the index in the array and the number of pairs you need

dp[i][k] = max(dp[i+1][k], dp[i+m][k-1] + sum(A[i], A[i+1], ... , A[i+m-1]) )