/* -*- coding: utf-8 -*- * * 3712.cc: No.3712 Urban Train - yukicoder */ #include #include #include #include #include using namespace std; /* constant */ const int MAX_N = 200000; const long long LINF = 1LL << 62; /* typedef */ using ll = long long; using pii = pair; using pli = pair; using vpii = vector; /* global variables */ vpii nbrs[MAX_N]; int as[MAX_N], bs[MAX_N], cs[MAX_N]; ll ds[MAX_N]; /* subroutines */ /* main */ int main() { int n, m; scanf("%d%d", &n, &m); for (int i = 0; i < m; i++) { int u, v, w; scanf("%d%d%d", &u, &v, &w); u--, v--; nbrs[u].push_back({v, w}); nbrs[v].push_back({u, w}); } for (int i = 0; i < n; i++) scanf("%d", as + i); for (int i = 0; i < n; i++) scanf("%d", bs + i); for (int i = 0; i < n; i++) scanf("%d", cs + i); fill(ds, ds + n, LINF); ds[0] = 1; priority_queue q; q.push({-ds[0], 0}); while (! q.empty()) { auto [ud, u] = q.top(); q.pop(); ud = -ud; if (ds[u] != ud) continue; if (u == n - 1) break; ll k = (ud + as[u] - 1) / as[u]; ll dt = k * as[u]; for (auto [v, w]: nbrs[u]) { ll vd = dt + w; if (k % bs[u] == 0) vd += min(cs[u], as[u]); if (ds[v] > vd) ds[v] = vd, q.push({-vd, v}); } } printf("%lld\n", ds[n - 1]); return 0; }