Description

Soon, Little W discovered that segment trees waste far too much space.

For example, a segment tree with $n=6$ looks like this:

You can see that only $11$ nodes store useful information, but the array indices used go up to $13$.

Let $f(n)$ be the maximum array index occupied by a segment tree with $n$ leaf nodes. Now Little W wants you to compute:

$$f(l)\;\oplus\;f(l+1)\;\oplus\;f(l+2)\;\oplus\cdots \oplus\;f(r)$$

Here, $\oplus$ denotes the bitwise XOR operation, which is the ^ operator in C++.

Input Format

One line with two integers $l, r$, with the meaning described above.

Output Format

One line with one integer, the result.

6 6

13

Hint

Sample Explanation

$f(6)=13$, so the answer is $13$.

Hint

If you do not know what a segment tree is:

void build(int k,int l,int r)
{
	if(l==r)
	{
		//do something
		//e.g. tree[k]=a[l]
		return;
	}
	int mid=(l+r)>>1;
	build(k<<1,l,mid);
	build(k<<1|1,mid+1,r);
	//do something
	//e.g. tree[k]=tree[k<<1]+tree[k<<1|1]
}

In plain words: node $k$ corresponds to a segment $[l,r]$. If $l\neq r$, let $mid=\lfloor\dfrac{l+r}2\rfloor$. It has two children: the left child has index $2k$ and segment $[l,mid]$; the right child has index $2k+1$ and segment $[mid+1,r]$. Then build the tree recursively on the child nodes.

After calling build(1,1,n), the segment tree is built. That is, node $1$ corresponds to segment $[1,n]$.

Constraints

For $10\%$ of the testdata, $1\le l\le r\le10^3$.
For $40\%$ of the testdata, $1\le l\le r\le 10^6$.
For $100\%$ of the testdata, $1\le l\le r\le10^{15}$, and the answer fits in long long.

Input Format

One line with two integers $l, r$, with the meaning described above.

Output Format

One line with one integer, the result.

Hint

Translated by ChatGPT 5