The marmots need to prepare k problems for HC² over n days. Each problem, once prepared, also has to be printed.

The preparation of a problem on day i (at most one per day) costs a_i CHF, and the printing of a problem on day i (also at most one per day) costs b_i CHF. Of course, a problem cannot be printed before it has been prepared (but doing both on the same day is fine).

What is the minimum cost of preparation and printing?

The first line of input contains two space-separated integers n and k (1≤k≤n≤2200). The second line contains n space-separated integers a₁,...,a_n () − the preparation costs. The third line contains n space-separated integers b₁,...,b_n () − the printing costs.

Output the minimum cost of preparation and printing k problems − that is, the minimum possible sum a_i1+a_i2+...+a_ik+b_j1+b_j2+...+b_jk, where 1≤i₁<i₂<...<i_k≤n, 1≤j₁<j₂<...<j_k≤n and i₁≤j₁, i₂≤j₂, ..., i_k≤j_k.