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 PYTHON3):

Solution:
N, D = map(int, input().split())
time = 0
floor = 1
num = 0
result = 0
for _ in [0]*N:
    t, f = map(int, input().split())
    if floor-1+f-1 <= t-time:
        result += num * (floor-1)
        num = 1
    elif abs(floor-f) <= t-time and num < D:
        result += num * abs(t-time)
        num += 1
    else:
        print(-1)
        break
    time, floor = t, f
else:
    result += num * (floor-1)
    print(result)