The ZAFT are attacking the Orb Union! There are ~I~ stations, numbered from ~1, 2, \dots, 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~. 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

Sample Output

1

Explanation for Sample Output

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.