1854C - Expected Destruction - CodeForces Solution

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

#define rep(i, a, b) for(int i = a; i < (b); ++i) 
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
#define pb push_back
#define F first
#define S second
#define mp make_pair
#define INP(v, n) for (int i=0; i<n; ++i) { cin >> v[i]; }
#define ceil(x) (ll)ceil(x)
#define floor(x) (ll)floor(x)

template<typename T> inline T maxe(vector<T> &vec) { return *max_element(all(vec)); }
template<typename T> inline T mine(vector<T> &vec) { return *min_element(all(vec)); }

struct custom_hash { // https://codeforces.com/blog/entry/62393
    static uint64_t splitmix64(uint64_t x) { x += 0x9e3779b97f4a7c15; x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9; x = (x ^ (x >> 27)) * 0x94d049bb133111eb; return x ^ (x >> 31); }
    size_t operator()(uint64_t x) const { static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count(); return splitmix64(x + FIXED_RANDOM); }
};
template<typename T, typename U> struct safe_map : public std::unordered_map<T,U,custom_hash> {};
template<typename T> struct safe_set : public std::unordered_set<T,custom_hash> {};

template<typename T> ostream& operator<<(ostream &os, const vector<T> &v) 
{ os << '{'; string sep; for (const auto &x: v) os << sep << x, sep = ", "; return os << '}';}
template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) 
{ return os << '(' << p.first << ", " << p.second << ')'; }

void dbg_out() { cerr << endl; }
template<typename Head, typename... Tail> void dbg_out(Head H, Tail... T) { cerr << ' ' << H; dbg_out(T...); }

#ifdef TTL
#define dbg(...) cerr << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif

template<typename T> inline void print(T obj) { cout << obj << '\n'; }
template<typename T, typename... Args> inline void print(T t, Args... args) { cout << t << " "; print(args...); }

typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;
typedef vector<int> VI;
typedef vector<int> vi; 
typedef vector<vector<int>> VVI;
typedef vector<long long> VLL;
typedef vector<vector<long long>> VVLL;
typedef vector<bool> VB;
typedef vector<vector<bool>> VVB;
typedef vector<string> VS;
typedef vector<vector<string>> VVS;
typedef pair<int, int> PII;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef vector<pair<int, int>> VPII;
typedef vector<vector<pair<int, int>>> VVPII;

VPII dirs{mp(-1,0),mp(1,0),mp(0,-1),mp(0,1)};
const ld pi = 3.1415926535897932384626433832795;
const ll mod = 1000000007;
// const ll mod = 998244353;


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() {
        // Ensures that 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 = 1000000007;
using mod_int = _m_int<MOD>;


vector<mod_int> _factorial = {1, 1}, _inv_factorial = {1, 1};

void prepare_factorials(int64_t maximum) {
    static int64_t prepared_maximum = 1;

    if (maximum <= prepared_maximum)
        return;

    // Prevent increasing maximum by only 1 each time.
    maximum += maximum / 64;
    _factorial.resize(maximum + 1);
    _inv_factorial.resize(maximum + 1);

    for (int64_t i = prepared_maximum + 1; i <= maximum; i++)
        _factorial[i] = i * _factorial[i - 1];

    _inv_factorial[maximum] = _factorial[maximum].inv();

    for (int64_t i = maximum - 1; i > prepared_maximum; i--)
        _inv_factorial[i] = (i + 1) * _inv_factorial[i + 1];

    prepared_maximum = maximum;
}

mod_int factorial(int64_t n) {
    if (n < 0) return 0;
    prepare_factorials(n);
    return _factorial[n];
}

mod_int inv_factorial(int64_t n) {
    if (n < 0) return 0;
    prepare_factorials(n);
    return _inv_factorial[n];
}

mod_int choose(int64_t n, int64_t r) {
    if (r < 0 || r > n) return 0;
    prepare_factorials(n);
    return _factorial[n] * _inv_factorial[r] * _inv_factorial[n - r];
}

mod_int permute(int64_t n, int64_t r) {
    if (r < 0 || r > n) return 0;
    prepare_factorials(n);
    return _factorial[n] * _inv_factorial[n - r];
}

mod_int inv_choose(int64_t n, int64_t r) {
    assert(0 <= r && r <= n);
    prepare_factorials(n);
    return _inv_factorial[n] * _factorial[r] * _factorial[n - r];
}

mod_int inv_permute(int64_t n, int64_t r) {
    assert(0 <= r && r <= n);
    prepare_factorials(n);
    return _inv_factorial[n] * _factorial[n - r];
}

void run() {
    ll n,m; cin >> n >> m; VLL v(n); INP(v,n);
    mod_int ans = m+1-v.back();
    rep(i,0,n-1) {
        ll a = (m+1-v[i+1]);
        ll b = (m+1-v[i]);
        vector<vector<mod_int>> dp(a+1, vector<mod_int>(b+1,0));
        dp[0][0] = 1;
        rep(j,0,a+1) {
            rep(k,0,b+1) {
                if (b-a < k-j) continue;
                if (b-a == k-j || (b-a)-(k-j) == 1) {
                    if (k>0) dp[j][k] = dp[j][k-1]/(j == a ? 1 : 2);
                }
                else {
                    if (k>0) dp[j][k] += dp[j][k-1]/(j==a ? 1 : 2);
                    if (j>0) dp[j][k] += dp[j-1][k]/(k==b ? 1 : 2);
                }
                if (b-a==k-j) {
                    ans += dp[j][k] * (b-a+j);
                }
            }
        }

    }
    print(ans);
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cin.exceptions(cin.failbit);
    // cout.setf(ios::fixed);
    // cout.precision(15);
    // ll t; cin >> t;
    ll t=1;
    rep(tests,0,t) run();
}