Calculate the number of sequences with K elements that meet the following criteria:   Each element is a positive integer ranging from L to R inclusive. All elements' bitwise XOR is ranging from A to B inclusive. Since the number of sequences matching the preceding constraints can be fairly big, compute it with modulo 998,244,353.   Input Format   Each test case's first and only line contains the five space-separated integers L, R, A, B, and K.   Constraints   0≤LR 2^60 0≤AB ≤ 2^60 1K50 Output Format   For each test case, output a single integer value denoting the number of sequences K modulo 998,244,353.   Sample Input:   26 54 18 34 1   Sample Output:   9   Explanation:   The number of sequences is given by 9.

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Calculate the number of sequences with K elements that meet the following criteria:
 
Each element is a positive integer ranging from L to R inclusive.
All elements' bitwise XOR is ranging from A to B inclusive.
Since the number of sequences matching the preceding constraints can be fairly big, compute it with modulo 998,244,353.
 
Input Format
 
Each test case's first and only line contains the five space-separated integers L, R, A, B, and K.
 
Constraints
 
0≤LR 2^60
0≤AB ≤ 2^60
1K50
Output Format
 
For each test case, output a single integer value denoting the number of sequences K modulo 998,244,353.
 
Sample Input:
 
26 54 18 34 1
 
Sample Output:
 
9
 
Explanation:
 
The number of sequences is given by 9.
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