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

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

```
$N$ $M$
```

Print the answer as an integer.

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

4

• popcount(0&3)=0
• popcount(1&3)=1
• popcount(2&3)=1
• popcount(3&3)=2
• popcount(4&3)=0

The sum of these values is 4.

0