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| #include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#include<vector>
#include<queue>
#include<set>
#include<map>
using namespace std;
typedef double db;
typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> pii;
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define sz(x) ((int)(x).size())
#define all(x) begin(x),end(x)
#define rep(i,l,r) for(int i=(l);i<(r);++i)
#define per(i,l,r) for(int i=(r)-1;i>=(l);--i)
#define dd(x) cout << #x << "=" << x << ", "
#define de(x) cout << #x << "=" << x << endl
const int P = 9973;
const int M = 10;
const int N = 31625;
int n, m, k;
vector<int> prime;
bool isprime[N];
struct Matrix {
int a[M][M];
void init(int x) {
rep(i, 0, m) rep(j, 0, m)
a[i][j] = i == j ? x : 0;
}
void fill(int x) {
rep(i, 0, m) rep(j, 0, m)
a[i][j] = x;
}
int trace() {
int ret = 0;
rep(i, 0, m) ret += a[i][i];
return ret % P;
}
Matrix operator*(const Matrix &mat) const {
Matrix r; r.init(0);
rep(i, 0, m) rep(j, 0, m) {
rep(k, 0, m) r.a[i][j] += a[i][k] * mat.a[k][j];
r.a[i][j] %= P;
}
return r;
}
Matrix operator^(int n) {
Matrix r, a = *this;
r.init(1);
while (n > 0) {
if (n & 1) r = r * a;
a = a * a, n >>= 1;
}
return r;
}
};
inline void inc(int &x, int y) {
if ((x += y) >= P) x -= P;
}
void initPrime() {
memset(isprime, 1, sizeof(isprime));
isprime[0] = isprime[1] = false;
rep(i, 2, N) {
if (isprime[i]) prime.push_back(i);
for (int j = 0; i * prime[j] < N; ++j) {
isprime[i * prime[j]] = false;
if (i % prime[j] == 0) break;
}
}
}
int phi(int n) {
int ret = n;
rep(i, 0, sz(prime)) {
if (n < prime[i]) break;
if (n % prime[i] == 0) {
ret -= ret / prime[i];
while (n % prime[i] == 0)
n /= prime[i];
}
}
if (n > 1) ret -= ret / n;
return ret;
}
int f(int n, int d, Matrix &a) {
int fd = (a ^ d).trace();
return phi(n / d) % P * fd % P;
}
void exgcd(int a, int b, int &x, int &y) {
if (!b) x = 1, y = 0;
else {
exgcd(b, a % b, y, x);
y -= a / b * x;
}
}
int inv(int n) {
int x, y;
exgcd(n, P, x, y);
x = (x % P + P) % P;
return x;
}
int main() {
initPrime();
int cases; scanf("%d", &cases);
while (cases-- > 0) {
scanf("%d%d%d", &n, &m, &k);
Matrix a; a.fill(1);
rep(_k, 0, k) {
int x, y; scanf("%d%d", &x, &y);
--x, --y;
a.a[x][y] = a.a[y][x] = 0;
}
int ans = 0;
for (int d = 1; d * d <= n; ++d) {
if (n % d) continue;
inc(ans, f(n, d, a));
if (d * d != n)
inc(ans, f(n, n / d, a));
}
ans = ans * inv(n) % P;
printf("%d\n", ans);
}
return 0;
}
|
