A9056. Fish Weight

It is known that there are $k$ fish species in the polar ocean, numbered from $1$ to $k$ . They are sorted by non-decreasing order of their weight, which is a positive number. Let the weight of the $i$ -th type of fish be $w_{i}$ , then $0<w_{1}<=w_{2}<=...<=w_{k}$ holds.

Polar bears Alice and Bob each have caught some fish, and they are guessing who has the larger sum of weight of the fish he/she's caught. Given the type of the fish they've caught, determine whether it is possible that the fish caught by Alice has a strictly larger total weight than Bob's. In other words, does there exist a sequence of weights $w_{i}$ (not necessary integers), such that the fish caught by Alice has a strictly larger total weight?

The first line contains three integers $n,m,k$ $(1<=n,m<=10^{5},1<=k<=10^{9})$ — the number of fish caught by Alice and Bob respectively, and the number of fish species.

The second line contains $n$ integers each from 1 to $k$ , the list of fish type caught by Alice. The third line contains $m$ integers each from 1 to $k$ , the list of fish type caught by Bob.

Note that one may have caught more than one fish for a same species.

Output "YES" (without quotes) if it is possible, and "NO" (without quotes) otherwise.

In the first sample, if $w_{1}=1,w_{2}=2,w_{3}=2.5$ , then Alice has a total of $2+2+2=6$ weight units, while Bob only has $1+1+2.5=4.5$ .

In the second sample, the fish that Alice caught is a subset of Bob's. Therefore, the total weight of Bob’s fish is always not less than the total weight of Alice’s fish.