Battle Positions

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Points: 7
Time limit: 2.0s
Memory limit: 128M

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Problem type

The ZAFT are attacking the Orb Union! There are I stations, numbered from (1, 2, \dots, I-1, I), that need to be defended. For it to be secure, the Orb Union needs to have at least N troops at each station. Unfortunately, due to the radar-jamming effects of the Neutron Jammer, the Orb Union cannot order their troops to move between stations. The Orb Union will send J waves of troops, each of which sends K troops to each of the stations (X_i, X_{i+1}, \dots, X_{f-1}, X_f). All stations start with 0 troops.

The Orb Union wants you to help them find the number of stations that are not secure.

Input Specification

The first line will contain the integer I (1 \le I \le 10^5), the number of stations.

The second line will contain the integer N (1 \le N \le 10^9), the minimum number of troops required to defend a station.

The third line will contain the integer J (1 \le J \le 10^5), the number of waves of troops.

The next J lines will contain 3 space-separated integers. These integers will be in the order X_i, X_f, K (1 \le X_i \le X_f \le I) (1 \le K \le 10^4).

Output Specification

Output the total number of stations that have less than N troops.

Sample Input

4
1
3
1 3 1
2 3 2
3 3 2

Output for Sample Input

1

Explanation of Output for Sample Input

Station 1 has 1 troop, station 2 has 3 troops, station 3 has 5 troops and station 4 has 0 troops. Station 4 is the only station with less than 1 troop, so the output is 1.


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