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 wi, then 0<w1≤w2≤...≤wk 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 wi (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≤105,1≤k≤109) − 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.
3 3 3
2 2 2
1 1 3
YES
4 7 9
5 2 7 3
3 5 2 7 3 8 7
NO
In the first sample, if w1=1,w2=2,w3=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.