#include <bits/stdc++.h>
using namespace std;
using ll = long long;
static constexpr int LIM = 20010;
static bitset<LIM> cop[LIM];
ll ans = 0;
void build_coprime_table() {
cop[1][0] = cop[1][1] = 1;
for (int i = 1; i < LIM; ++i) {
for (int j = 0; j <= i; ++j) {
if (i == 1 && j <= 1) continue;
if (i - j > j) cop[i][j] = cop[i - j][j];
else cop[i][j] = cop[j][i - j];
}
}
}
inline bool visible(int x, int y) {
if (x < y) swap(x, y);
while (y && (x >= LIM || y >= LIM)) {
int nx = y;
int ny = x % y;
x = nx;
y = ny;
}
if (!y) return x == 1;
return cop[x][y];
}
void dfs(ll x, ll y, int k, int dx, int dy) {
for (int i = 0; i < k; ++i) {
x += dx;
y += dy;
ans += visible((int)x, (int)y);
}
if ((dx == 0 || dy == 0) && k == 1) return;
if (dx == 0) {
dfs(x, y, k >> 1, -1, dy);
dfs(x, y, k >> 1, 1, dy);
} else if (dy == 0) {
dfs(x, y, k >> 1, dx, -1);
dfs(x, y, k >> 1, dx, 1);
} else {
dfs(x, y, k, dx, 0);
dfs(x, y, k, 0, dy);
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
build_coprime_table();
int M, N, F;
cin >> M >> N >> F;
while (F--) {
int x, y, k;
cin >> x >> y >> k;
--x; --y; // switch to 0-based coordinates
ans += visible(x, y); // starting tree
dfs(x, y, k, -1, 0); // first move is north
}
cout << ans << '\n';
return 0;
}
