B'Getting closer and closer to a mathematician, Serval becomes a university student on math major in Japari University. On the Calculus class, his teacher taught him how to calculate the expected length of a random subsegment of a given segment. Then he left a bonus problem as homework, with the award of a garage kit from IOI. The bonus is to extend this problem to the general case as follows. You are given a segment with length l . We randomly choose n segments by choosing two points (maybe with non-integer coordinates) from the given segment equiprobably and the interval between the two points forms a segment. You are given the number of random segments n , and another integer k . The 2n endpoints of the chosen segments split the segment into (2n+1) intervals. Your task is to calculate the expected total length of those intervals that are covered by at least k segments of the n random segments. You should find the answer modulo 998244353 . First line contains three space-separated positive integers n , k and l ( 1 <= q k <= q n <= q 2000 , 1 <= q l <= q 10^9 ). Output one integer -- the expected total length of all the intervals covered by at least k segments of the n random segments modulo 998244353 . Formally, let M = 998244353 . It can be shown that the answer can be expressed as an irreducible fraction frac{p}{q} , where p and q are integers and q not equiv 0 pmod{M} . Output the integer equal to p cdot q^{-1} bmod M . In other words, output such an integer x that 0 <= x < M and x cdot q equiv p pmod{M} . In the first example, the expected total length is int_0^1 int_0^1 |x-y| , mathrm{d}x , mathrm{d}y = {1 over 3} , and 3^{-1} modulo 998244353 is 332748118 . '...