Problem Statement

The computer game Toaru Fantasy manages various numerical values using $N$-bit signed integers (two's complement).

An overflow bug was recently found in Toaru Fantasy, and strategies exploiting it are being studied.
Normally, you defeat an enemy by attacking it and bringing its HP down to 0 or below.
In the overflow bug strategy, on the other hand, you defeat an enemy by deliberately healing its HP, taking advantage of the fact that the enemy is also judged as defeated when its HP becomes 0 or below due to overflow.

Let $X$ be the enemy's initial HP, $A$ be the amount of HP reduced by one attack, and $B$ be the amount of HP increased by one heal.
Each attack and each heal takes 1 unit of time. Find the minimum time required to defeat the enemy.
The enemy never increases or decreases its own HP.

Information for those unfamiliar with two's complement

An integer $x (-2^{N-1} \leq x < 2^{N-1})$ can be represented as an $N$-bit signed integer using a bit sequence $a_{n-1}, a_{n-2}, \dots, a_{3}, a_{2}, a_{1}$ ($a_i$ = 0 or 1) such that
$$ x = - 2^{n-1} * a_{n-1} + \sum_{k=0}^{k < n-1} 2^k * a_k $$
(see also: binary numeral system)

In other words, the value represented by each bit is as shown in the table below.

 bit  |   N-1  |  N-2  | ... | 3 | 2 | 1 | 0 
------|--------|-------|-----|---|---|---|---
value |-2^(N-1)|2^(N-2)| ... | 8 | 4 | 2 | 1 

Addition of two integers $x,y (-2^{N-1} \leq x,y < 2^{N-1})$ works the same way as with ordinary integer types. Any part that goes beyond the most significant bit (carry flag) is ignored.
https://en.wikipedia.org/wiki/Two%27s_complement#Addition

In pseudocode, it looks like this.

// Bit Array A + B => C
carry = 0
for i in [0, N) :
    C[i] = (A[i] + B[i] + carry) % 2
    carry = floor( (A[i] + B[i] + carry) / 2 )

return C

Input

$N$
$X$
$A$
$B$

The first line gives the bit length $N$ of the integer type used in the game.
The second line gives the enemy's initial HP $X$.
The third line gives the amount $A$ of HP reduced by one attack.
The fourth line gives the amount $B$ of HP increased by one heal.

All inputs are given as integers.
$2\leq N \leq 32$
$1\leq X,A,B < 2^{N-1}$

Output

Output the minimum time required to defeat the enemy.

Sample

4
4
3
1

2

  0100 ( 敵の体力 4 )
+)1101 ( -A(=-3) を 2 の補数で表現 )
------
  0001 ( 残り体力 1 )

  0001 ( 敵の体力 1 )
+)1101 ( -A(=-3) を 2 の補数で表現 )
------
  1110 ( 残り体力 -2 )

4
6
2
1

2

  0110 ( 敵の体力 6 )
+)0001 ( B(=1) )
------
  0111 ( 残り体力 7 )

  0111 ( 敵の体力 7 )
+)0001 ( B(=1) )
------
  1000 ( 残り体力 -8 )

26
16777221
20
20

838861