#include #include #include #include #include using namespace std; using i32 = int; using u32 = unsigned int; using i64 = long long; using u64 = unsigned long long; #define rep(i,n) for(int i=0; i<(int)(n); i++) using m32 = atcoder::static_modint<1000000007>; i64 isqrt(i64 x){ i64 l = 0, r = 2001001001; while(l + 1 < r){ i64 m = (l+r) / 2; if(m * m <= x) l = m; else r = m; } return l; } const m32 inv2 = m32(2).inv(); const m32 inv6 = m32(6).inv(); m32 linear_sum(i64 x){ return m32(x) * (m32(x)+1) * inv2; } m32 square_sum(i64 x){ return m32(x) * (m32(x)+1) * (m32(x)*2+1) * inv6; } // sum_{i=0}^N ceil(i*i/a) m32 solve2(i64 a, i64 N){ //cout << "a = " << a << " , N = " << N << endl; m32 ans = 0; for(i64 b=0; b> a >> N; i64 n = isqrt(a * N); m32 grid = m32(n) * m32(N); return grid - solve2(a, n); } int main(){ int T; cin >> T; rep(t,T) cout << solve().val() << '\n'; return 0; } struct ios_do_not_sync{ ios_do_not_sync(){ std::ios::sync_with_stdio(false); std::cin.tie(nullptr); } } ios_do_not_sync_instance;