一个蒙哥马利约减

来源：https://www.luogu.com.cn/record/210348683

template<uint32_t mod>struct LazyMontgomeryModInt{using mint=LazyMontgomeryModInt;using i32=int32_t;using u32=uint32_t;using u64=uint64_t;static constexpr u32 get_r(){u32 ret=mod;for(i32 i=0;i<4;++i)ret*=2-mod*ret;return ret;}static constexpr u32 r=get_r();static constexpr u32 n2=-u64(mod)%mod;static_assert(r*mod==1,"invalid, r * mod != 1");static_assert(mod<(1<<30),"invalid, mod >= 2 ^ 30");static_assert((mod&1)==1,"invalid, mod % 2 == 0");u32 a;constexpr LazyMontgomeryModInt():a(0){}constexpr LazyMontgomeryModInt(const int64_t&b):a(reduce(u64(b%mod+mod)*n2)){};static constexpr u32 reduce(const u64&b){return(b+u64(u32(b)*u32(-r))*mod)>>32;}constexpr mint&operator+=(const mint&b){if(i32(a+=b.a-2*mod)<0)a+=2*mod;return*this;}constexpr mint&operator-=(const mint&b){if(i32(a-=b.a)<0)a+=2*mod;return*this;}constexpr mint&operator*=(const mint&b){a=reduce(u64(a)*b.a);return*this;}constexpr mint&operator/=(const mint&b){*this*=b.inverse();return*this;}constexpr mint operator+(const mint&b)const{return mint(*this)+=b;}constexpr mint operator-(const mint&b)const{return mint(*this)-=b;}constexpr mint operator*(const mint&b)const{return mint(*this)*=b;}constexpr mint operator/(const mint&b)const{return mint(*this)/=b;}constexpr bool operator==(const mint&b)const{return(a>=mod?a-mod:a)==(b.a>=mod?b.a-mod:b.a);}constexpr bool operator!=(const mint&b)const{return(a>=mod?a-mod:a)!=(b.a>=mod?b.a-mod:b.a);}constexpr mint operator-()const{return mint()-mint(*this);}constexpr mint pow(u64 n)const{mint ret(1),mul(*this);while(n>0){if(n&1)ret*=mul;mul*=mul;n>>=1;}return ret;}constexpr mint inverse()const{return pow(mod-2);}friend ostream&operator<<(ostream&os,const mint&b){return os<<b.get();}friend istream&operator>>(istream&is,mint&b){int64_t t;is>>t;b=LazyMontgomeryModInt<mod>(t);return(is);}constexpr u32 get()const{u32 ret=reduce(a);return ret>=mod?ret-mod:ret;}static constexpr u32 get_mod(){return mod;}explicit operator u32()const{return get();}};
#define modint LazyMontgomeryModInt
#define mint modint<998244353>

注意它的构造函数是接受 int64_t 的