The First Galactic Fleet flagship Eltreum was patrolling near
the center of the Milky Way. Unidentified ships appeared in this sector
some time ago and the crew of Eltreum kept a close watch on them.
All ships have been counted and classified by the Universal
Military Classifier, but their mission and identity remained unclear.
Suddenly, after nearly a week of staying at one place the unidentified ships began to move.
Some of them went straight into hyperspace, and one of the remaining ships activated a
jamming device that rendered Eltreum's radars useless.
Visual observation showed that all the remaining ships rushed away from
Eltreum, lining up in a chain in nondescending order of their classes:
the lightest ships were ahead and the heaviest ships closed the
procession. Unfortunately, only one of the ships in this chain has been
precisely identified—the one with a jammer device. The classes of the other ships were not identified.
But, perhaps, information gained from the visual observation could help infer something about the remaining ships, couldn't it?
Input
The first line contains integers n and t that is the number of
unidentified ships before and after the hyperjump (1 ≤ t < n ≤ 5000).
The second line contains integers c_{1}, …, c_{n} that are the classes
of the ships according to the Universal Military Classifier (1 ≤ c_{i} ≤ 5000).
The third line contains integers k and x: the number of the identified ship and its position in the chain (1 ≤ k ≤ n;
1 ≤ x ≤ t). The number of the identified ship is its position in the list in the second line. Chain positions are numbered from the head of the procession, that is, the list begins with the smallest class number.
Output
Output the number of possible sets of the remaining
ships modulo 10^{9} + 7.
Samples
input  output 

5 3
2 1 1 3 1
2 3
 1

4 2
1 1 1 1
1 2
 3

Notes
In the first example only the set {2, 3, 5} of ships could remain after the hyperleap. In the second example the following sets could remain: {1, 2}, {1, 3}, {1, 4}.
Problem Author: Alex Samsonov (prepared by Alexander Fetisov)
Problem Source: Ural Championship 2012