The Legend Was Invented, but Not the Name

You are given two numbers $x$ and $y$. You need to find an array of numbers such that the sum of the squares of these numbers is equal to $10^{15}+x$, and the sum of the cubes is equal to $10^{15}+y$. Formally, you need to find any array of numbers such that:

where $m$ is the number of elements in this array.

Input

The first and only line contains two integers $x$ and $y$ ($0\le x,y\le 10^9$).

Output

In the first line, you need to output only one integer $n$ $(1\le n\le 2\cdot 10^5)$ — the number of distinct elements in the array $a$.

In the next $n$ lines you need to output the information about the array in the following form:

$c_i{k}_i$

That means that there are $k_i$ elements in the array that are equal to $c_i$ $(1\le i\le n,1\le c_i\le 10^9,1\le k_i\le 10^{16})$.

All $c_i$'s need to be pairwise distinct.

If there are multiple answers, you can output any of them.

If there are no needed arrays, you need to output $-1$.

Examples

Note

In the first example, there are $10^{15}-3$ elements equal to $1$ and $1$ element equal to $2$. This way, the sums are following:

$(10^{15}-3)\cdot 1^2+1\cdot 2^2=10^{15}+1$

$(10^{15}-3)\cdot 1^3+1\cdot 2^3=10^{15}+5$

In the second example, there are $10^{15}+1$ $1$'s and $1$ entry of each number from $2$ to $5$:

$(10^{15}+1)\cdot 1^2+1\cdot 2^2+1\cdot 3^2+1\cdot 4^2+1\cdot 5^2=(10^{15}+1)+4+9+16+25=10^{15}+55$

$(10^{15}+1)\cdot 1^3+1\cdot 2^3+1\cdot 3^3+1\cdot 4^3+1\cdot 5^3=(10^{15}+1)+8+27+64+125=10^{15}+225$

In the third sample, it can be shown that there are no arrays that would satisfy the conditions.

Scoring

1. ($12$ points): $x=y$;

2. ($13$ points): $x>y$;

3. ($76$ points): $x,y\le 99999$;

4. ($99$ points): no additional constraints.