Operator Party

A variable $X$ that holds an integer starts at $0$.

For each $i$ from $1$ to $N$, increasing by $1$ each time, perform the operations that match the conditions below. After finishing all operations up to $N$, print the final value of $X$.

• If $i$ is a multiple of $A$, do $X$ = $X$ + $i$. (+ is the addition operator.)
• If $i$ is a multiple of $B$, do $X$ = $X$ % $i$. (% is the remainder operator.)
• If $i$ is a multiple of $C$, do $X$ = $X$ & $i$. (& is the bitwise AND operator.)
• If $i$ is a multiple of $D$, do $X$ = $X$ ⊕ $i$. (⊕ is the bitwise XOR operator.)
• If $i$ is a multiple of $E$, do $X$ = $X$ | $i$. (| is the bitwise OR operator.)
• If $i$ is a multiple of $F$, do $X$ = $X$ >> $i$. (>> is the bitwise right shift operator.)
• When several operations apply at once, perform them in the priority order +, %, &, ⊕, |, >>.

The first line contains $N$.

The second line contains $A$, $B$, $C$, $D$, $E$, and $F$, separated by spaces.

Print the final value of $X$.

• $1 \le N \le 10^{12}$
• $1 \le A \le B \le C \le D \le E \le F \le 1\,000\,000$
• $N$, $A$, $B$, $C$, $D$, $E$, and $F$ are positive integers.

Bitwise operators work on each bit separately.

Bitwise AND

For each pair of bits, the result bit is $1$ only when both bits are $1$. Otherwise it is $0$.

Example: $\begin{aligned} 0110_{2} &= 6 \\ \text{\&} \ \ 1100_{2} &= 12 \\ \text{────} \\ 0100_{2} &= 4 \end{aligned}$

Bitwise XOR

For each pair of bits, the result bit is $1$ when the two bits differ. Otherwise it is $0$.

Example: $\begin{aligned} 0110_{2} &= 6 \\ \text{⊕} \ \ 1100_{2} &= 12 \\ \text{────} \\ 1010_{2} &= 10 \end{aligned}$

Bitwise OR

For each pair of bits, the result bit is $1$ when at least one of the bits is $1$. Otherwise it is $0$.

Example: $\begin{aligned} 0110_{2} &= 6 \\ \text{|} \ \ 1100_{2} &= 12 \\ \text{────} \\ 1110_{2} &= 14 \end{aligned}$

Bitwise right shift

For $a$ >> $b$, the bits of $a$ move $b$ places to the right. The bits that open up on the left are filled with $0$.

Example: $\begin{aligned} & 0110_{2} \ \text{>>} \ 2 \\ & \downarrow \\ & 0001_{2} \end{aligned}$