How would you go about solving this variation of Knapsack?

You have n objects (x1,...xn), each with cost ci and value vi (1<=i<=n) and an additional constraint X, which is a lower bound on the value of the items selected.
Find a subset of x1,...,xn that minimizes the cost of the items with a value of at least X.

I am trying to solve this through Dynamic Programming, and what I thought of was to modify the usual table used into K[n,c,X] where X would be the minimum value I need to reach, but that seems to bring me nowhere. Any good ideas?