AT_abc431_c [ABC431C] Robot Factory

Takahashi can combine a head part and a body part to create a robot. A robot falls over if the weight of the head part is greater than the weight of the body part. Currently, he has $ N $ head parts and $ M $ body parts. The weight of the $ i $ -th $ (1\le i\le N) $ head part is $ H _ i $ grams, and the weight of the $ i $ -th $ (1\le i\le M) $ body part is $ B _ i $ grams. He wants to create a total of $ K $ robots that do not fall over by appropriately combining the parts he has. Determine whether he can achieve his goal by combining the parts well. Here, a part cannot be used to create multiple robots, and two or more head parts (or two or more body parts) cannot be used to create one robot.

The input is given from Standard Input in the following format: > $ N $ $ M $ $ K $ $ H _ 1 $ $ H _ 2 $ $ \ldots $ $ H _ N $ $ B _ 1 $ $ B _ 2 $ $ \ldots $ $ B _ M $

Print `Yes` if Takahashi can combine the parts well to create $ K $ robots that do not fall over; otherwise, print `No`.

### Sample Explanation 1 If we denote combining the $ i $ -th head part and the $ j $ -th body part as $ (i,j) $ , then Takahashi can create three robots that do not fall over by combining them as $ (1,2),(2,4),(3,6) $ , for example. Thus, print `Yes`. ### Sample Explanation 2 His head part is too heavy, so he cannot create any robot that does not fall over. ### Sample Explanation 3 Note that a robot does not fall over if the head and body have equal weights. ### Constraints - $ 1\le N\le2\times10 ^ 5 $ - $ 1\le M\le2\times10 ^ 5 $ - $ 1\le K\le\min\lbrace N,M\rbrace $ - $ 1\le H _ i\le10 ^ 9\ (1\le i\le N) $ - $ 1\le B _ i\le10 ^ 9\ (1\le i\le M) $ - All input values are integers.