#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #pragma warning (disable: 4996) using namespace std; using ll = long long; unsigned euclidean_gcd(unsigned a, unsigned b) { if (a < b) return euclidean_gcd(b, a); unsigned r; while ((r = a % b)) { a = b; b = r; } return b; } ll ll_gcd(ll a, ll b) { if (a < b) return ll_gcd(b, a); ll r; while ((r = a % b)) { a = b; b = r; } return b; } struct UnionFind { vector par; vector siz; UnionFind(ll sz_) : par(sz_), siz(sz_, 1LL) { for (ll i = 0; i < sz_; ++i) par[i] = i; } void init(ll sz_) { par.resize(sz_); siz.assign(sz_, 1LL); for (ll i = 0; i < sz_; ++i) par[i] = i; } ll root(ll x) { while (par[x] != x) { x = par[x] = par[par[x]]; } return x; } bool merge(ll x, ll y) { x = root(x); y = root(y); if (x == y) return false; if (siz[x] < siz[y]) swap(x, y); siz[x] += siz[y]; par[y] = x; return true; } bool issame(ll x, ll y) { return root(x) == root(y); } ll size(ll x) { return siz[root(x)]; } }; long long modpow(long long a, long long n, long long mod) { if (n < 0)return 0; long long res = 1; while (n > 0) { if (n & 1) res = res * a % mod; a = a * a % mod; n >>= 1; } return res; } long long modinv(long long a, long long mod) { return modpow(a, mod - 2, mod); } ll merge_cnt(vector& a) { int n = a.size(); if (n <= 1) { return 0; } ll cnt = 0; vector b(a.begin(), a.begin() + n / 2); vector c(a.begin() + n / 2, a.end()); cnt += merge_cnt(b); cnt += merge_cnt(c); int ai = 0, bi = 0, ci = 0; while (ai < n) { if (bi < b.size() && (ci == c.size() || b[bi] <= c[ci])) { a[ai++] = b[bi++]; } else { cnt += n / 2 - bi; a[ai++] = c[ci++]; } } return cnt; } struct edge { ll to, cost; }; typedef pair P; struct graph { ll V; vector > G; vector d; graph(ll n) { init(n); } void init(ll n) { V = n; G.resize(V); d.resize(V); for (int i = 0; i < V; i++) { d[i] = 2000000000000000000; } } void add_edge(ll s, ll t, ll cost) { edge e; e.to = t, e.cost = cost; G[s].push_back(e); } void dijkstra(ll s) { for (int i = 0; i < V; i++) { d[i] = 2000000000000000000; } d[s] = 0; priority_queue, greater

> que; que.push(P(0, s)); while (!que.empty()) { P p = que.top(); que.pop(); ll v = p.second; if (d[v] < p.first) continue; for (auto e : G[v]) { if (d[e.to] > d[v] + e.cost) { d[e.to] = d[v] + e.cost; que.push(P(d[e.to], e.to)); } } } } }; int main() { ll n,m; cin >> n >> m; m -= 3; vector z(n+1); for (int i = 0; i < n-1; i++) { cin >> z[i + 2]; z[i + 2]--; } ll ans = 0; for (int i = 2; i < n; i++) { if (n % i != 0)continue; for (int j = 2; j < n/i; j++) { if (n % (i*j) != 0)continue; vector x(3); x[0] = z[n]; x[1] = z[j*i]; x[2] = z[i]; sort(x.begin(), x.end()); ll f = (modpow(x[2], m + 1, 1000000007) - modpow(x[1], m + 1, 1000000007) + 1000000007) * modinv(x[2] - x[1], 1000000007) % 1000000007 * x[1] % 1000000007; ll g= (modpow(x[2], m + 1, 1000000007) - modpow(x[0], m + 1, 1000000007) + 1000000007) * modinv(x[2] - x[0], 1000000007) % 1000000007 * x[0] % 1000000007; ans+=(f-g+1000000007) * modinv(x[1] - x[0], 1000000007) % 1000000007; } } ans %= 1000000007; ll q; cin >> q; set f; vector> d(n+1); for (int i = 0; i < q; i++) { cout << ans << endl; ll a, b; cin >> a >> b; d[b].push_back(a); if (b == n) { f.insert(a); for (int i = 2; i <= sqrt(a); i++) { if (a % i != 0)continue; if (i != sqrt(a)) { vector x(3); x[0] = z[n]; x[1] = z[a/i]; x[2] = z[a]; sort(x.begin(), x.end()); ll f = (modpow(x[2], m + 1, 1000000007) - modpow(x[1], m + 1, 1000000007) + 1000000007) * modinv(x[2] - x[1], 1000000007) % 1000000007 * x[1] % 1000000007; ll g = (modpow(x[2], m + 1, 1000000007) - modpow(x[0], m + 1, 1000000007) + 1000000007) * modinv(x[2] - x[0], 1000000007) % 1000000007 * x[0] % 1000000007; ans += (f - g + 1000000007) * modinv(x[1] - x[0], 1000000007) % 1000000007; } vector x(3); x[0] = z[n]; x[1] = z[a]; x[2] = z[i]; sort(x.begin(), x.end()); ll f = (modpow(x[2], m + 1, 1000000007) - modpow(x[1], m + 1, 1000000007) + 1000000007) * modinv(x[2] - x[1], 1000000007) % 1000000007 * x[1] % 1000000007; ll g = (modpow(x[2], m + 1, 1000000007) - modpow(x[0], m + 1, 1000000007) + 1000000007) * modinv(x[2] - x[0], 1000000007) % 1000000007 * x[0] % 1000000007; ans += (f - g + 1000000007) * modinv(x[1] - x[0], 1000000007) % 1000000007; } for (int i = 0; i < d[a].size(); i++) { vector x(3); x[0] = z[n]; x[1] = z[a]; x[2] = z[d[a][i]]; sort(x.begin(), x.end()); ll f = (modpow(x[2], m + 1, 1000000007) - modpow(x[1], m + 1, 1000000007) + 1000000007) * modinv(x[2] - x[1], 1000000007) % 1000000007 * x[1] % 1000000007; ll g = (modpow(x[2], m + 1, 1000000007) - modpow(x[0], m + 1, 1000000007) + 1000000007) * modinv(x[2] - x[0], 1000000007) % 1000000007 * x[0] % 1000000007; ans += (f - g + 1000000007) * modinv(x[1] - x[0], 1000000007) % 1000000007; } } else if (f.count(b)||n%b==0) { vector x(3); x[0] = z[n]; x[1] = z[a]; x[2] = z[b]; sort(x.begin(), x.end()); ll f = (modpow(x[2], m + 1, 1000000007) - modpow(x[1], m + 1, 1000000007) + 1000000007) * modinv(x[2] - x[1], 1000000007) % 1000000007 * x[1] % 1000000007; ll g = (modpow(x[2], m + 1, 1000000007) - modpow(x[0], m + 1, 1000000007) + 1000000007) * modinv(x[2] - x[0], 1000000007) % 1000000007 * x[0] % 1000000007; ans += (f - g + 1000000007) * modinv(x[1] - x[0], 1000000007) % 1000000007; } ans %= 1000000007; } cout << ans << endl; }