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struct mi {
typedef decay<decltype(MOD)>::type T;
/// don't silently convert to T
T v; explicit operator T() const { return v; }
mi() { v = 0; }
mi(ll _v) {
v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
if (v < 0) v += MOD;
}
friend bool operator==(const mi& a, const mi& b) {
return a.v == b.v; }
friend bool operator!=(const mi& a, const mi& b) {
return !(a == b); }
friend bool operator<(const mi& a, const mi& b) {
return a.v < b.v; }
friend void re(mi& a) { ll x; re(x); a = mi(x); }
friend str ts(mi a) { return ts(a.v); }
mi& operator+=(const mi& m) {
if ((v += m.v) >= MOD) v -= MOD;
return *this; }
mi& operator-=(const mi& m) {
if ((v -= m.v) < 0) v += MOD;
return *this; }
mi& operator*=(const mi& m) {
v = (ll)v*m.v%MOD; return *this; }
mi& operator/=(const mi& m) { return (*this) *= inv(m); }
friend mi pow(mi a, ll p) {
mi ans = 1; assert(p >= 0);
for (; p; p /= 2, a *= a) if (p&1) ans *= a;
return ans;
}
friend mi inv(const mi& a) { assert(a.v != 0);
return pow(a,MOD-2); }
mi operator-() const { return mi(-v); }
mi& operator++() { return *this += 1; }
mi& operator--() { return *this -= 1; }
friend mi operator+(mi a, const mi& b) { return a += b; }
friend mi operator-(mi a, const mi& b) { return a -= b; }
friend mi operator*(mi a, const mi& b) { return a *= b; }
friend mi operator/(mi a, const mi& b) { return a /= b; }
};
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