Problem Statement

Iwai Seijin wants to be satisfied by the next programming contest, "ABC10000". Your job as the contest organizer is to adopt good problems from among the problem proposals while at the same time satisfying Iwai Seijin.

There are $N$ problem proposals, numbered $1, 2, ..., N$.
When problem proposal $i$ is adopted, Iwai Seijin gains $A_i$ of satisfaction. ($A_i$ may be negative.)
Also, problem proposal $i$ has a beauty of $C_i$.

Output the maximum satisfaction Iwai Seijin can gain when $D$ distinct problem proposals are adopted so that the total beauty is at least $K$.
However, if the total beauty cannot be at least $K$, output No.

Constraints

• $1\leq D\leq N\leq 500$
• $1\leq K\leq 500$
• $-10^9\leq A_i\leq 10^9$
• $0\leq C_i\leq 10^9$
• All input values are integers.

Input

The input is given from standard input in the following format.

$N\quad D\quad K$
$A_1\quad A_2\quad ... \quad A_{N-1} \quad A_N$
$C_1\quad C_2\quad ... \quad C_{N-1} \quad C_N$

Output

Output the maximum satisfaction that meets the conditions.
If it is impossible to meet the conditions, output No.

Sample

5 3 20
20 10 -15 30 20
3 8 11 9 6

60

1 1 500
3
10

No

16 8 240
101 -202 300 400 -430 700 -720 820 -830 -890 910 -970 990 1013 -1250 1270
50 20 15 35 25 30 35 40 20 30 10 35 0 20 35 20

4494