Problem Statement

Given integers N and M, compute the sum $\displaystyle \sum_{k=0}^{N} \rm{popcount}(k \mathbin{$\&} M), modulo 998244353.
Here, $\mathbin{$\&} represents the bitwise $\rm{AND}$ operation.
What is the bitwise $\rm{AND}$ operation?
The result $x = a \mathbin{$\&} b of the bitwise $\rm{AND} operation between non-negative integers a$ and b is defined as follows:

• x is the unique non-negative integer that satisfies the following conditions for all non-negative integers k:

• If the 2^k place in the binary representation of a and the 2^k place in the binary representation of b are both 1, then the 2^k place in the binary representation of x is 1.

• Otherwise, the 2^k place in the binary representation of x is 0.

For example, 3=11_{(2)} and 5=101_{(2)}, so $3 \mathbin{$\&} 5 = 1.

What is $\rm{popcount}$?
$\rm{popcount}(x)$ represents the number of 1s in the binary representation of x.
For example, 13=1101_{(2)}, so $\rm{popcount}(13) = 3$.

Input

The input is given from Standard Input in the following format:
N M

Output

Print the answer as an integer.

Constraints

• N is an integer between 0 and 2^{60} - 1, inclusive.
• M is an integer between 0 and 2^{60} - 1, inclusive.

Sample Input 1

4 3

Sample Output 1

4

• $\rm{popcount}(0\mathbin{$\&}3) = 0
• $\rm{popcount}(1\mathbin{$\&}3) = 1
• $\rm{popcount}(2\mathbin{$\&}3) = 1
• $\rm{popcount}(3\mathbin{$\&}3) = 2
• $\rm{popcount}(4\mathbin{$\&}3) = 0

The sum of these values is 4.

Sample Input 2

0 0

Sample Output 2

0

It is possible that N = 0 or M = 0.

Sample Input 3

1152921504606846975 1152921504606846975

Sample Output 3

499791890

Remember to compute the result modulo 998244353.

见题面 Input 部分

见题面 Output 部分