问题 F: Educational Problem II

You are given n, m, l, r and a matrix B = (bi,j )n×m. Count the number of integer sequence a1, a2, . . . , an satisfying the following conditions, modulo 998 244 353: • ∀i ∈ Z ∩ [1, n], l ≤ ai ≤ r. • ∀i ∈ Z ∩ [1, n], ∃S ⊆ Z ∩ [1, m], ai = L j∈S bi,j . That is, ai is equal to the bitwise XOR sum of some subsequence of (bi,1, bi,2, . . . , bi,m), and ai = 0 if the subsequence is empty. • The number of i ∈ Z ∩ [2, n] that ai−1 6= ai is minimized among all the sequences satisfying the above two conditions.

The first line contains four integers n, m, l, r (2 ≤ n ≤ 105 , 2 ≤ nm2 ≤ 4 × 107 , 0 ≤ l ≤ r < 2 m). The i-th of the following n lines contains m integers bi,1, bi,2, . . . , bi,m (0 ≤ bi,j < 2 m). Please note that l, r, bi,j are given in binary notation length of m. 

Output an integer representing the answer.

3 2 01 10
01 00
01 10
00 10

2