Double Summation of Divisor Function under XOR

Given three integers n, m, and x, compute the value of

\( S = \sum_{i=0}^{n} \sum_{j=0}^{m} d\bigl(i\operatorname{xor}j\operatorname{xor}x\bigr) \)

where \( \operatorname{xor} \) denotes the bitwise XOR operation, and \( d(y) \) denotes the number of positive divisors of y (with the convention that \( d(0)=0 \)). Since the answer can be large, output the result modulo \( 998244353 \).

inputFormat

The input consists of a single line containing three space-separated integers \( n \), \( m \), and \( x \).

outputFormat

Output a single integer, the value of \( S \) modulo \( 998244353 \).

sample

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