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神仙反演题。在洛谷上疯狂被卡常

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#include<bits/stdc++.h>

#define Pair pair<int, int>

#define MP make_pair

#define fi first

#define se second

#define LL long long 

const int MAXN = 2e5 + 10, mod = 1e9 + 7;

using namespace std;

template <typename A, typename B> inline bool chmin(A &a, B b){if(a > b) {a = b; return 1;} return 0;}

template <typename A, typename B> inline bool chmax(A &a, B b){if(a < b) {a = b; return 1;} return 0;}

template <typename A, typename B> inline LL add(A x, B y) {if(x + y < 0) return x + y + mod; return x + y >= mod ? x + y - mod : x + y;}

template <typename A, typename B> inline void add2(A &x, B y) {if(x + y < 0) x = x + y + mod; else x = (x + y >= mod ? x + y - mod : x + y);}

template <typename A, typename B> inline LL mul(A x, B y) {return 1ll * x * y % mod;}

template <typename A, typename B> inline void mul2(A &x, B y) {x = (1ll * x * y % mod + mod) % mod;}

inline int read() {

	char c = getchar(); int x = 0, f = 1;

	while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}

	while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();

	return x * f;

}

int mu[MAXN], prime[MAXN], vis[MAXN], tot, A, B, C, num, deg[MAXN];

int fa[MAXN], fb[MAXN], fc[MAXN];

vector<LL> di[MAXN];

vector<Pair> v[MAXN];//每个数的质因数分解

struct Edge {

	LL u, v, w;

}E[MAXN * 10];

void GetPrime(int N) {

	vis[1] = 1; mu[1] = 1;

	for(int i = 2; i <= N; i++) {

		if(!vis[i]) prime[++tot] = i, mu[i] = -1;

		for(int j = 1; j <= tot && i * prime[j] <= N; j++) {

			vis[i * prime[j]] = 1;

			if(i % prime[j]) mu[i * prime[j]] = -mu[i];

			else {mu[i * prime[j]] = 0; break;}

		}

	}

	for(int i = 1; i <= tot; i++)

		for(int j = 1; j * prime[i] <= N; j++)

			di[j * prime[i]].push_back(prime[i]);

}

void Get(int *a, int N, int X) {

	for(int i = 1; i <= N; i++)

		for(int j = i; j <= N; j += i) a[i] += X / j;

}

LL lcm(int a, int b) {

	return 1ll * a / __gcd(a, b) * b;

}

void init() {

	memset(fa, 0, sizeof(fa));

	memset(fb, 0, sizeof(fb));

	memset(fc, 0, sizeof(fc));

	memset(deg, 0, sizeof(deg));

	num = 0;

	for(int i = 1; i <= A; i++) v[i].clear();

}

void Build() {

	for(int w = 1; w <= A; w++) {//lcm(u, v) = w;

		if(!mu[w]) continue;

		int n = di[w].size();

		//for(auto x : di[w]) printf("%d ", x); puts("");

		for(int sta = 0; sta < (1 << n); sta++) {

			LL i = 1;

			for(int b = 0; b < n; b++)

				if(sta >> b & 1) i *= di[w][b];

			for(int s = sta; ; s = sta & (s - 1)) {//tag

				LL g = 1;

				for(int b = 0; b < n; b++)

					if(s >> b & 1)

						g *= di[w][b];

				int j = w * g / i;

				if(i < j) E[++num] = {i, j, w};// printf("%d\n", num);

				if(!s) break;

			}

		}

	}

}

LL fuck(int x, int y, int w) {

	if(mu[x] == 1)

		return add(add(mul(mul(fa[w], fb[w]), fc[y]), mul(mul(fa[w], fb[y]), fc[w])), mul(mul(fa[y], fb[w]), fc[w]));

	else

		return (-add(add(mul(mul(fa[w], fb[w]), fc[y]), mul(mul(fa[w], fb[y]), fc[w])), mul(mul(fa[y], fb[w]), fc[w])) + mod) % mod;

}

LL calc() {

//	for(int i = 1; i <= A; i++) for(auto &x : v[i])printf("%d %d %d\n", i, x.fi, x.se);

	for(int i = 1; i <= num; i++) {

		int x = E[i].u, y = E[i].v;

		if(deg[x] > deg[y]) swap(x, y);

		v[y].push_back(MP(x, E[i].w));

	}

	LL ans = 0;

	for(int a = 1; a <= A; a++) {

		for(auto &t1 : v[a]) {

			LL b = t1.fi, w1 = t1.se;

			for(auto &t2 : v[b]) {

				LL c = t2.fi, w2 = t2.se, xi = mu[a] * mu[b] * mu[c];

				LL w3 = lcm(a, c);

				if(w3 > A) continue;

				if(xi == 1) {

					add2(ans, mul(mul(fa[w1], fb[w2]), fc[w3]));

					add2(ans, mul(mul(fa[w1], fb[w3]), fc[w2]));

					add2(ans, mul(mul(fa[w2], fb[w1]), fc[w3]));

					add2(ans, mul(mul(fa[w2], fb[w3]), fc[w1]));

					add2(ans, mul(mul(fa[w3], fb[w1]), fc[w2]));

					add2(ans, mul(mul(fa[w3], fb[w2]), fc[w1]));

				} else if(xi == -1) {

					add2(ans, mul(mul(-fa[w1], fb[w2]), fc[w3]));

					add2(ans, mul(mul(-fa[w1], fb[w3]), fc[w2]));

					add2(ans, mul(mul(-fa[w2], fb[w1]), fc[w3]));

					add2(ans, mul(mul(-fa[w2], fb[w3]), fc[w1]));

					add2(ans, mul(mul(-fa[w3], fb[w1]), fc[w2]));

					add2(ans, mul(mul(-fa[w3], fb[w2]), fc[w1]));

				}

			//	cout << ans << endl;

			}

		}

	}

	for(int i = 1; i <= num; i++) {//有两个一样

		add2(ans, fuck(E[i].u, E[i].v, E[i].w));

		add2(ans, fuck(E[i].v, E[i].u, E[i].w));

	}

	for(int i = 1; i <= C; i++) {//全都一样

		if(mu[i] == 1) add2(ans, mul(mul(fa[i], fb[i]), fc[i]));

		else if(mu[i] == -1) add2(ans, -mul(mul(fa[i], fb[i]), fc[i]) + mod);

	}

	return ans;

}

void solve() {

	init();

	A = read(); B = read(); C = read();

	if(A < B) swap(A, B); if(C > B) swap(B, C); if(A < B) swap(A, B);

	Get(fa, A, A); Get(fb, A, B); Get(fc, A, C);

	Build();

	cout << calc() << '\n';

}

signed main() {

//	freopen("gg1.txt", "w", stdout);

	GetPrime(2e5);

	for(int T = read(); T; T--, solve());

	return 0;

}