#include using namespace std; #define rep(i, n) for (int i = 0; i < n; i++) #define rep2(i, x, n) for (int i = x; i <= n; i++) #define rep3(i, x, n) for (int i = x; i >= n; i--) #define each(e, v) for (auto &e : v) #define pb push_back #define eb emplace_back #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; const int MOD = 1000000007; // const int MOD = 998244353; const int inf = (1 << 30) - 1; const ll INF = (1LL << 60) - 1; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; template struct Mod_Int { int x; Mod_Int() : x(0) {} Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} static int get_mod() { return mod; } Mod_Int &operator+=(const Mod_Int &p) { if ((x += p.x) >= mod) x -= mod; return *this; } Mod_Int &operator-=(const Mod_Int &p) { if ((x += mod - p.x) >= mod) x -= mod; return *this; } Mod_Int &operator*=(const Mod_Int &p) { x = (int)(1LL * x * p.x % mod); return *this; } Mod_Int &operator/=(const Mod_Int &p) { *this *= p.inverse(); return *this; } Mod_Int &operator++() { return *this += Mod_Int(1); } Mod_Int operator++(int) { Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int &operator--() { return *this -= Mod_Int(1); } Mod_Int operator--(int) { Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator-() const { return Mod_Int(-x); } Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; } Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; } Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; } Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; } bool operator==(const Mod_Int &p) const { return x == p.x; } bool operator!=(const Mod_Int &p) const { return x != p.x; } Mod_Int inverse() const { assert(*this != Mod_Int(0)); return pow(mod - 2); } Mod_Int pow(long long k) const { Mod_Int now = *this, ret = 1; for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; } friend istream &operator>>(istream &is, Mod_Int &p) { long long a; is >> a; p = Mod_Int(a); return is; } }; using mint = Mod_Int; template struct Combination { static vector _fac, _ifac; Combination() {} static void init(int n) { _fac.resize(n + 1), _ifac.resize(n + 1); _fac[0] = 1; for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i; _ifac[n] = _fac[n].inverse(); for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i; } static T fac(int k) { return _fac[k]; } static T ifac(int k) { return _ifac[k]; } static T inv(int k) { return fac(k - 1) * ifac(k); } static T P(int n, int k) { if (k < 0 || n < k) return 0; return fac(n) * ifac(n - k); } static T C(int n, int k) { if (k < 0 || n < k) return 0; return fac(n) * ifac(n - k) * ifac(k); } static T H(int n, int k) { // k個の区別できない玉をn個の区別できる箱に入れる場合の数 if (n < 0 || k < 0) return 0; return k == 0 ? 1 : C(n + k - 1, k); } static T second_stirling_number(int n, int k) { // n個の区別できる玉を、k個の区別しない箱に、各箱に1個以上玉が入るように入れる場合の数 T ret = 0; for (int i = 0; i <= k; i++) { T tmp = C(k, i) * T(i).pow(n); ret += ((k - i) & 1) ? -tmp : tmp; } return ret * ifac(k); } static T bell_number(int n, int k) { // n個の区別できる玉を、k個の区別しない箱に入れる場合の数 if (n == 0) return 1; k = min(k, n); vector pref(k + 1); pref[0] = 1; for (int i = 1; i <= k; i++) { if (i & 1) pref[i] = pref[i - 1] - ifac(i); else pref[i] = pref[i - 1] + ifac(i); } T ret = 0; for (int i = 1; i <= k; i++) { ret += T(i).pow(n) * ifac(i) * pref[k - i]; } return ret; } }; template vector Combination::_fac = vector(); template vector Combination::_ifac = vector(); using comb = Combination; int main() { int N, M; cin >> N >> M; comb::init(3000000); mint S = 0; rep2(i, M, N) S += comb::C(N, i); mint ans = S * N; rep2(i, M, N) ans += comb::C(N, i) * (2 * i - N); // cout << ans << '\n'; vector s(N + 2, 0); rep2(i, 0, N) s[i + 1] = s[i] + comb::C(N, i); vector dp(N + 1, 0); // dp[N] = S; rep2(i, 0, N) { int l = (N - i) / 2; if ((N - i) & 1) { int x = l; chmax(l, M); if (l <= N) dp[i] += s[N - l + 1]; if (2 * x - l >= 0) dp[i] -= s[2 * x - l + 1]; } else { int x = l; chmax(l, M); if (l <= N) dp[i] += s[N - l + 1]; if (2 * x - l - 1 >= 0) dp[i] -= s[2 * x - l]; } } rep2(i, 1, N) ans += (dp[i] - dp[i - 1]) * i * 2; cout << ans << '\n'; }