In a large farm, N ducks are standing and making a big circle. They are numbered 1 to N. Their position are sorted in clockwise and the N^th duck is adjacent to the first duck.

Then, they will make a game with the following rules:

• The game is played in N rounds.
• The first round is to decide who is the N^th winner, second round is to decide who is the (N-1)^th winner and so on until N^th round is to decide who is the champion (1^st winner). formally, i^th round is to decide who is the (N-i+1)^th winner.
• In each round i (1 ≤ i ≤ N), Mr. Dengklek as a moderator counting the ducks in clockwise direction. A_i^th duck will be the winner in this round, that duck will not play anymore and get out from the circle.
• In the first round, Mr. Dengklek starts counting from the first duck. Then in i^th round (1 < i ≤ N), Mr. Dengklek will start counting from the duck after the previous round winner.

A is an array of N integer with A₁ = L. For 1 < i ≤ N, if A_i-1 = R then A_i = L. Otherwise, A_i = A_i-1 + 1.

Because the number of ducks is too large, so the game won't be finished even though in one century. Here, you are to find the fastest algorithm to know the M^th winner (with given N, L, and R) in less than 2 seconds.

Input

Input contains 2 lines only.

In the first line, given N and M separated by a white space.

The last line contain 2 integers represent L and R.

Output

The only line contain one number represent the M^th winner of that game.

Constraints

1 ≤ M ≤ N ≤ 10¹⁸

1 ≤ L ≤ R ≤ 10¹⁸

N-M ≤ 10⁸ or R ≤ 10⁵

Example

Input:
5 3
2 4
Output:
1

Explanation

A = {2,3,4,2,3}

round 1:
    1 - 2
    second duck become the 5^th winner and get out from the game.
round 2:
    3 - 4 - 5
    start counting from 3^th duck because the previous winner is the second duck.
round 3:
    1 - 3 - 4 - 1
    after the last duck is the first duck because they are standing in a circle.
    second duck and 5^th duck skipped because they are not playing anymore.
round 4:
    3 - 4
    A₄ = L = 2 because A₃ = 4 = R.
round 5:
    3 - 3 - 3
    3^th duck is the champion.