There're n stores selling m kinds of items. Each store only sells one kind of item, the i-th store sells the ai-th kind of item. You're going to buy some items. You do the following operation k times: choose a store at random,and buy one item from that store. Let there are ci stores selling item i. After all the operations, you will get unsatisfied, if and only if the following condition is satisfied: • There exists an item i, where you hold exact ci of them, and they are all from different stores. For example, if store 1 and 3 are selling item 1, and after operations, you hold exactly two items 1, and one of them is from store 1, where the other one is from store 3, you will get unsatisfied. You want to know the possibility of not getting unsatisfied after k operations. Output it modulo 998244353.
输入格式
The first line contains the number of test cases T(1 ≤ T ≤ 100). For each test case: The first line contains three integers: n, m, k(1 ≤ m ≤ n ≤ 2 × 105,1 ≤ k < 998244353). The following line contains n integers a1, a2 . . . an(1 ≤ ai ≤ m). It is guaranteed that each of the m kinds of items will appear at least once. There will be no more than 10 test cases where n ≥ 104.