CodeForces - 567D One-Dimensional Battle Ships

E - One-Dimensional Battle Ships

CodeForces - 567D

Alice and Bob love playing one-dimensional battle ships. They play on the field in the form of a line consisting of n square cells (that is, on a 1 × n table).

At the beginning of the game Alice puts k ships on the field without telling their positions to Bob. Each ship looks as a 1 × a rectangle (that is, it occupies a sequence of a consecutive squares of the field). The ships cannot intersect and even touch each other.

After that Bob makes a sequence of "shots". He names cells of the field and Alice either says that the cell is empty ("miss"), or that the cell belongs to some ship ("hit").

But here's the problem! Alice like to cheat. May be that is why she responds to each Bob's move with a "miss".

Help Bob catch Alice cheating — find Bob's first move, such that after it you can be sure that Alice cheated.

Input

The first line of the input contains three integers: n, k and a (1 ≤ n, k, a ≤ 2·10⁵) — the size of the field, the number of the ships and the size of each ship. It is guaranteed that the n, k and a are such that you can put k ships of size a on the field, so that no two ships intersect or touch each other.

The second line contains integer m (1 ≤ m ≤ n) — the number of Bob's moves.

The third line contains m distinct integers x₁, x₂, ..., x_m, where x_i is the number of the cell where Bob made the i-th shot. The cells are numbered from left to right from 1 to n.

Output

Print a single integer — the number of such Bob's first move, after which you can be sure that Alice lied. Bob's moves are numbered from 1 to m in the order the were made. If the sought move doesn't exist, then print "-1".

Examples

Input

11 3 3
5
4 8 6 1 11

Output

3

Input

5 1 3
2
1 5

Output

-1

Input

5 1 3
1
3

Output

1

ID-OJ:
codeforces-567D

author:
Caution_X

DATE of submission:
20,191,031

Tags:
Analog

description modelling:
given map 1 × N, the boat has a k on the map, each boat space 1 × a, and now the number m of input each number indicates whether the check. xi xi position must have a boat. Output: If the i-th check will be able to check out the ship, the output i

Major Steps to Solve IT:
(. 1) First discharge: given an interval [1, N], provided this interval up to put the number of vessels x, then x * a + (x-. 1) = N
=> x = (N +. 1) / (a +. 1)
(2) is not the first place: provided check the x-th position, then we can put the vessel section to in [(1, x-1) and x + 1, N],
then referred to sum to check the number of vessels in step i can be released, then the implementation of the x-th check sum = sum - (rl) / (a + 1) + (xl) / ( a + 1) + (rx) / (a + 1), if sum <k, then the i-th step will be found the ship inspection, output i

the AC code:

#include <iostream>
#include <cstring>
#include <cstdio>
#include <algorithm>
#include <set>
using namespace std;

set<int> s;

int main ()
{
    int m, n, a, k, x;
    while (scanf("%d%d%d", &n, &k, &a) != EOF) {
        scanf("%d", &m);
        s.clear();
        s.insert ( 0 ), s.insert (n-+ . 1 );    // implement virtual tips length 
        int SUM = (n-+ . 1 ) / (A + . 1 ); 
         int ANS = - . 1 , F = 0 ;
         for ( int I = . 1 ; I <= m; I ++ ) {
            scanf("%d", &x);
            set<int>::iterator it = s.upper_bound(x);
            int r = *it;
            int l = *(--it);
            sum = sum - (r-l)/(a+1) +(x-l)/(a+1) + (r-x)/(a+1);

            if (sum < k && !f) {
                years = i;
                f = 1;
            }
            s.insert(x);
        }
        printf("%d\n", ans);
    }
    return 0;
}