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?

Input

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 ( $\text{[math]}$ ) — the preparation costs. The third line contains n space-separated integers b₁, ..., b_n ( $\text{[math]}$ ) — the printing costs.

Output

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

Note

In the sample testcase, one optimum solution is to prepare the first problem on day 1 and print it on day 1, prepare the second problem on day 2 and print it on day 4, prepare the third problem on day 3 and print it on day 5, and prepare the fourth problem on day 6 and print it on day 8.

April Fools' Problem (medium)

Examples