Problem: problem

AOR Co., Ltd. (Association Of Return home) has $ N $ employees.

Employee $ i $ wants to use the elevator to go down to the $ 1 $ floor and arrives in front of the elevator on the $ F_i $ floor at time $ t_i $. You decide to remotely control an elevator that has only $ 1 $ on the $ 1 $ floor at time $ 0 $ and send all employees to the $ 1 $ floor. The elevator can only carry up to $ D $ people. Elevators can move upstairs or stay in place per unit time. Employee $ i $ only takes the elevator if the elevator is on the $ F_i $ floor at time $ t_i $ and does not exceed capacity. When I can't get on the elevator at time $ t_i $, I'm on the stairs to the $ 1 $ floor. The time it takes to get on and off can be ignored.

Find the minimum total time each employee is in the elevator. However, if there are even $ 1 $ people who cannot take the elevator to the $ 1 $ floor, output $ -1 $.



output

Output the minimum total time each employee is in the elevator. However, if there are even $ 1 $ people who cannot take the elevator to the $ 1 $ floor, output $ -1 $. Also, output a line break at the end.

Example

Input

2 2
2 2
3 3


Output

5

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define REP(i,n) for (int i=0;i<(n);i++)
#define REP2(i,m,n) for (int i=m;i<(n);i++)
typedef long long ll;


int main() {
    ll N, D; cin >> N >> D;
    ll pos = 1;
    ll time = 0;
    ll d = 0;
    ll ans = 0;

    REP(i, N) {
        ll t, f; cin >> t >> f;
        if (abs(f - pos) > t - time) {
            cout << -1 << endl;
            return 0;
        }

        if (d > 0 && time + pos + f - 2 <= t) {
            ans += (pos - 1) * d;
            pos = f;
            d = 1;
            time = t;
        } else {
            ans += (t - time) * d;
            pos = f;
            d += 1;
            time = t;
            if (d > D) {
                cout << -1 << endl;
                return 0;
            }
        }
    }

    ans += (pos - 1) * d;
    cout << ans << endl;
}