In other words, the symbol $\texttt{<expr>}$ can be the variable $a$, or a value that matches the definition of $\texttt{<num>}$, or a binary expression in parentheses, where each operand also matches the same definition of $\texttt{<expr>}$.

In the definition above, the symbol $\texttt{<num>}$ denotes a non-negative decimal integer strictly less than $2^n$. The symbol $\texttt{<operator>}$ can be $\texttt{+}$, $\texttt{-}$, $\texttt{|}$, $\texttt{\&}$, $\texttt{<<}$, or $\texttt{>>}$, which represent addition, subtraction, bitwise OR, bitwise AND, left shift, and right shift, respectively.

In addition, the character $a$ may appear at most $5$ times in $\texttt{<expr>}$.

If overflow or underflow occurs during addition or subtraction, MalnarScript performs these operations modulo $2^n$. For example, when $n = 3$, in MalnarScript, $7 + 3 = 2$, and $2 - 5 = 5$.

For each command, the expression on the right-hand side is evaluated to a number, and then stored into $a$. To compute the right-hand-side expression, MalnarScript first replaces every occurrence of $a$ with its current value. Then it evaluates the expression like in any mathematical expression, i.e. parentheses first. Note that operator precedence (the order among operators) is irrelevant, because the final result is fully determined by the placement of parentheses.

Your task is to write a program in MalnarScript that computes the popcount of the binary representation of the input value.

Input Format

The first line contains two positive integers $n, k$, with the meanings described in Description.

Output Format

In the first line, you should output the number of commands in the produced MalnarScript program.

In the remaining lines, you should output the commands of the required program. Each command must be output on its own line and must satisfy the MalnarScript syntax described in the task statement.

It is important that there are no unnecessary blank lines or extra space characters in the output. Each line (including the last line) must end with a newline (\n).

2 2

1
A=(A-((A&2)>>1))

3 5

2
A=((A&4)|((A&3)-((A&2)>>1)))
A=((A&3)+((A&4)>>2))

Hint

Constraints and Notes

Notes

The scoring of this problem follows the original COCI problem, with full score $110$.

Translated from COCI2019-2020 CONTEST #2 T4 Popcount.

Thanks to

In addition, because the testlib library has an issue when generating random numbers in the Luogu environment for $N = 31$, fixed pre-generated random numbers are used instead. For some test points with large $N$, the Special Judge program runs for a longer time, as follows.

The time limits above are only for the Special Judge program.

Translated by ChatGPT 5