Any finger appears at most once in S.

を読み落としていてひたすら悩んでいた。

## implementation

#include <cstdio>
#include <vector>
#include <algorithm>
#include <tuple>
#include <functional>
#define repeat(i, n) for (int i = 0; (i) < int(n); ++(i))
#define whole(f, x, ...) ([&](decltype((x)) whole) { return (f)(begin(whole), end(whole), ## __VA_ARGS__); })(x)
using ll = long long;
using namespace std;

vector<vector<int> > opposite_graph(vector<vector<int> > const & g) {
int n = g.size();
vector<vector<int> > h(n);
repeat (i, n) for (int j : g[i]) h[j].push_back(i);
return h;
}
pair<int, vector<int> > decompose_to_strongly_connected_components(vector<vector<int> > const & g, vector<vector<int> > const & g_rev) {
int n = g.size();
vector<int> acc(n); {
vector<bool> used(n);
function<void (int)> dfs = [&](int i) {
used[i] = true;
for (int j : g[i]) if (not used[j]) dfs(j);
acc.push_back(i);
};
repeat (i,n) if (not used[i]) dfs(i);
whole(reverse, acc);
}
int size = 0;
vector<int> component_of(n); {
vector<bool> used(n);
function<void (int)> rdfs = [&](int i) {
used[i] = true;
component_of[i] = size;
for (int j : g_rev[i]) if (not used[j]) rdfs(j);
};
for (int i : acc) if (not used[i]) {
rdfs(i);
++ size;
}
}
return { size, move(component_of) };
}
vector<vector<int> > decomposed_graph(int size, vector<int> const & component_of, vector<vector<int> > const & g) {
int n = g.size();
vector<vector<int> > h(size);
repeat (i, n) for (int j : g[i]) {
if (component_of[i] != component_of[j]) {
h[component_of[i]].push_back(component_of[j]);
}
}
repeat (k, size) {
whole(sort, h[k]);
h[k].erase(whole(unique, h[k]), h[k].end());
}
return h;
}

constexpr int mod = 1e9+7;
int main() {
int n, m; scanf("%d%d", &n, &m);
vector<vector<int> > g(n);
repeat (i, m) {
int s, d; scanf("%d%d", &s, &d); -- s; -- d;
g[s].push_back(d);
}
int size; vector<int> component_of; tie(size, component_of) = decompose_to_strongly_connected_components(g, opposite_graph(g));
vector<vector<int> > h = decomposed_graph(size, component_of, g);
vector<vector<int> > h_rev = opposite_graph(h);
int result = 1;
function<int (int)> go = [&](int i) {
int acc = 1;
for (int j : h_rev[i]) {
acc = acc *(ll) go(j) % mod;
}
return acc + 1;
};
repeat (i, size) {
if (h[i].empty()) {
result = result *(ll) go(i) % mod;
}
}
printf("%d\n", result);
return 0;
}