D.cpp

#include <bits/stdc++.h>
using namespace std;

#define nl '\n'

template<const int &MOD>
struct _m_int {
    int val;
 
    _m_int(int64_t v = 0) {
        if (v < 0) v = v % MOD + MOD;
        if (v >= MOD) v %= MOD;
        val = int(v);
    }
 
    _m_int(uint64_t v) {
        if (v >= MOD) v %= MOD;
        val = int(v);
    }
 
    _m_int(int v) : _m_int(int64_t(v)) {}
    _m_int(unsigned v) : _m_int(uint64_t(v)) {}
 
    explicit operator int() const { return val; }
    explicit operator unsigned() const { return val; }
    explicit operator int64_t() const { return val; }
    explicit operator uint64_t() const { return val; }
    explicit operator double() const { return val; }
    explicit operator long double() const { return val; }
 
    _m_int& operator+=(const _m_int &other) {
        val -= MOD - other.val;
        if (val < 0) val += MOD;
        return *this;
    }
 
    _m_int& operator-=(const _m_int &other) {
        val -= other.val;
        if (val < 0) val += MOD;
        return *this;
    }
 
    static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
    #if !defined(_WIN32) || defined(_WIN64)
        return unsigned(x % m);
    #endif
        // Optimized mod for Codeforces 32-bit machines.
        // x must be less than 2^32 * m for this to work, so that x / m fits in an unsigned 32-bit int.
        unsigned x_high = unsigned(x >> 32), x_low = unsigned(x);
        unsigned quot, rem;
        asm("divl %4\n"
            : "=a" (quot), "=d" (rem)
            : "d" (x_high), "a" (x_low), "r" (m));
        return rem;
    }
 
    _m_int& operator*=(const _m_int &other) {
        val = fast_mod(uint64_t(val) * other.val);
        return *this;
    }
 
    _m_int& operator/=(const _m_int &other) {
        return *this *= other.inv();
    }
 
    friend _m_int operator+(const _m_int &a, const _m_int &b) { return _m_int(a) += b; }
    friend _m_int operator-(const _m_int &a, const _m_int &b) { return _m_int(a) -= b; }
    friend _m_int operator*(const _m_int &a, const _m_int &b) { return _m_int(a) *= b; }
    friend _m_int operator/(const _m_int &a, const _m_int &b) { return _m_int(a) /= b; }
 
    _m_int& operator++() {
        val = val == MOD - 1 ? 0 : val + 1;
        return *this;
    }
 
    _m_int& operator--() {
        val = val == 0 ? MOD - 1 : val - 1;
        return *this;
    }
 
    _m_int operator++(int) { _m_int before = *this; ++*this; return before; }
    _m_int operator--(int) { _m_int before = *this; --*this; return before; }
 
    _m_int operator-() const {
        return val == 0 ? 0 : MOD - val;
    }
 
    friend bool operator==(const _m_int &a, const _m_int &b) { return a.val == b.val; }
    friend bool operator!=(const _m_int &a, const _m_int &b) { return a.val != b.val; }
    friend bool operator<(const _m_int &a, const _m_int &b) { return a.val < b.val; }
    friend bool operator>(const _m_int &a, const _m_int &b) { return a.val > b.val; }
    friend bool operator<=(const _m_int &a, const _m_int &b) { return a.val <= b.val; }
    friend bool operator>=(const _m_int &a, const _m_int &b) { return a.val >= b.val; }
 
    static const int SAVE_INV = int(1e6) + 5;
    static _m_int save_inv[SAVE_INV];
 
    static void prepare_inv() {
        // Make sure MOD is prime, which is necessary for the inverse algorithm below.
        for (int64_t p = 2; p * p <= MOD; p += p % 2 + 1)
            assert(MOD % p != 0);
 
        save_inv[0] = 0;
        save_inv[1] = 1;
 
        for (int i = 2; i < SAVE_INV; i++)
            save_inv[i] = save_inv[MOD % i] * (MOD - MOD / i);
    }
 
    _m_int inv() const {
        if (save_inv[1] == 0)
            prepare_inv();
 
        if (val < SAVE_INV)
            return save_inv[val];
 
        _m_int product = 1;
        int v = val;
 
        while (v >= SAVE_INV) {
            product *= MOD - MOD / v;
            v = MOD % v;
        }
 
        return product * save_inv[v];
    }
 
    _m_int pow(int64_t p) const {
        if (p < 0)
            return inv().pow(-p);
 
        _m_int a = *this, result = 1;
 
        while (p > 0) {
            if (p & 1)
                result *= a;
 
            p >>= 1;
 
            if (p > 0)
                a *= a;
        }
 
        return result;
    }
 
    friend ostream& operator<<(ostream &os, const _m_int &m) {
        return os << m.val;
    }
};
 
template<const int &MOD> _m_int<MOD> _m_int<MOD>::save_inv[_m_int<MOD>::SAVE_INV];
 
extern const int MOD = int(1e9) + 7;
using mod_int = _m_int<MOD>;


//----------------------------------- DEBUG -----------------------------------
#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifdef LOCAL
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
  ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
  *this << "[";
  for (auto it = d.b; it != d.e; ++it)
    *this << ", " + 2 * (it == d.b) << *it;
  ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
};
#define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
// debug & operator << (debug & dd, P p) { dd << "(" << p.x << ", " << p.y << ")"; return dd; }

//----------------------------------- END DEBUG --------------------------------

void run_cases() {
    int N, M;
    cin >> N >> M;

    vector<pair<int,int>> edges;

    vector<vector<int>> adj(N);
    for(int i = 0; i < M; i++) {
        int a, b;
        cin >> a >> b;
        --a, --b;
        adj[a].push_back(b);
        adj[b].push_back(a);
        edges.emplace_back(a, b);
    }

    vector<bool> vis(N, false);
    vector<int> levels(N, 0);

    vector<int> q;
    q.push_back(0);
    vis[0] = true;
    for(int i = 0; i < q.size(); i++) {
        int x = q[i];
        for(int child: adj[x]) {
            if(!vis[child]) {
                vis[child] = true;
                q.push_back(child);
                levels[child] = levels[x] + 1;
            }
        }
    }

    debug() << imie(levels);

    vector<vector<int>> dag(N);
    vector<int> indeg(N, 0);
    vector<int> t(N, N + 100);
    for(auto [a, b] : edges) {
        if(levels[a] > levels[b]) {
            swap(a, b);
        }
        dag[a].push_back(b);
        debug() << imie(a) imie(b);
        indeg[b]++;
    }
    t[0] = 0;
    q.clear();
    q.push_back(0);
    vector<mod_int> paths(N);
    paths[0] = 1;
    for(int i = 0; i < q.size(); i++) {
        int x = q[i];
        for(int child: dag[x]) {
            if(t[x] + 1 <= t[child]) {
                if(t[x] + 1 == t[child]) {
                    paths[child] += paths[x];
                } else {
                    t[child] = t[x] + 1;
                    paths[child] = paths[x];
                }
            }
            indeg[child]--;
            if(indeg[child] == 0) {
                q.push_back(child);
            }
        }
    }

    cout << paths[N - 1] << '\n';
}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(nullptr);

    int tests = 1;
    // cin >> tests;

    for(int test = 1;test <= tests;test++) {
        run_cases();
    }
}