高精度テンプレートclass

#define MAX_L 1005  // ， 
class bign {
public:
    int len, s[MAX_L];  // ， 
                        // 
    bign();
    bign(const char *);
    bign(int);
    bool sign;                                      //  1  0 
    string toStr() const;                           // ， 
    friend istream &operator>>(istream &, bign &);  // 
    friend ostream &operator<<(ostream &, bign &);  // 
                                                    // 
    bign operator=(const char *);
    bign operator=(int);
    bign operator=(const string);
    // 
    bool operator>(const bign &) const;
    bool operator>=(const bign &) const;
    bool operator<(const bign &) const;
    bool operator<=(const bign &) const;
    bool operator==(const bign &) const;
    bool operator!=(const bign &) const;
    // 
    bign operator+(const bign &) const;
    bign operator++();
    bign operator++(int);
    bign operator+=(const bign &);
    bign operator-(const bign &) const;
    bign operator--();
    bign operator--(int);
    bign operator-=(const bign &);
    bign operator*(const bign &)const;
    bign operator*(const int num) const;
    bign operator*=(const bign &);
    bign operator/(const bign &) const;
    bign operator/=(const bign &);
    // 
    bign operator%(const bign &) const;  // （ ）
    bign factorial() const;              // 
    bign Sqrt() const;                   // （ ）
    bign pow(const bign &) const;        // 
                                         // 
    void clean();
    ~bign();
};
#define max(a, b) a > b ? a : b
#define min(a, b) a < b ? a : b
bign::bign() {
    memset(s, 0, sizeof(s));
    len = 1;
    sign = 1;
}
bign::bign(const char *num) { *this = num; }
bign::bign(int num) { *this = num; }
string bign::toStr() const {
    string res;
    res = "";
    for (int i = 0; i < len; i++) res = (char)(s[i] + '0') + res;
    if (res == "")
        res = "0";
    if (!sign && res != "0")
        res = "-" + res;
    return res;
}
istream &operator>>(istream &in, bign &num) {
    string str;
    in >> str;
    num = str;
    return in;
}
ostream &operator<<(ostream &out, bign &num) {
    out << num.toStr();
    return out;
}
bign bign::operator=(const char *num) {
    memset(s, 0, sizeof(s));
    char a[MAX_L] = "";
    if (num[0] != '-')
        strcpy(a, num);
    else
        for (int i = 1; i < strlen(num); i++) a[i - 1] = num[i];
    sign = !(num[0] == '-');
    len = strlen(a);
    for (int i = 0; i < strlen(a); i++) s[i] = a[len - i - 1] - 48;
    return *this;
}
bign bign::operator=(int num) {
    char temp[MAX_L];
    sprintf(temp, "%d", num);
    *this = temp;
    return *this;
}
bign bign::operator=(const string num) {
    const char *tmp;
    tmp = num.c_str();
    *this = tmp;
    return *this;
}
bool bign::operator<(const bign &num) const {
    if (sign ^ num.sign)
        return num.sign;
    if (len != num.len)
        return len < num.len;
    for (int i = len - 1; i >= 0; i--)
        if (s[i] != num.s[i])
            return sign ? (s[i] < num.s[i]) : (!(s[i] < num.s[i]));
    return !sign;
}
bool bign::operator>(const bign &num) const { return num < *this; }
bool bign::operator<=(const bign &num) const { return !(*this > num); }
bool bign::operator>=(const bign &num) const { return !(*this < num); }
bool bign::operator!=(const bign &num) const { return *this > num || *this < num; }
bool bign::operator==(const bign &num) const { return !(num != *this); }
bign bign::operator+(const bign &num) const {
    if (sign ^ num.sign) {
        bign tmp = sign ? num : *this;
        tmp.sign = 1;
        return sign ? *this - tmp : num - tmp;
    }
    bign result;
    result.len = 0;
    int temp = 0;
    for (int i = 0; temp || i < (max(len, num.len)); i++) {
        int t = s[i] + num.s[i] + temp;
        result.s[result.len++] = t % 10;
        temp = t / 10;
    }
    result.sign = sign;
    return result;
}
bign bign::operator++() {
    *this = *this + 1;
    return *this;
}
bign bign::operator++(int) {
    bign old = *this;
    ++(*this);
    return old;
}
bign bign::operator+=(const bign &num) {
    *this = *this + num;
    return *this;
}
bign bign::operator-(const bign &num) const {
    bign b = num, a = *this;
    if (!num.sign && !sign) {
        b.sign = 1;
        a.sign = 1;
        return b - a;
    }
    if (!b.sign) {
        b.sign = 1;
        return a + b;
    }
    if (!a.sign) {
        a.sign = 1;
        b = bign(0) - (a + b);
        return b;
    }
    if (a < b) {
        bign c = (b - a);
        c.sign = false;
        return c;
    }
    bign result;
    result.len = 0;
    for (int i = 0, g = 0; i < a.len; i++) {
        int x = a.s[i] - g;
        if (i < b.len)
            x -= b.s[i];
        if (x >= 0)
            g = 0;
        else {
            g = 1;
            x += 10;
        }
        result.s[result.len++] = x;
    }
    result.clean();
    return result;
}
bign bign::operator*(const bign &num) const {
    bign result;
    result.len = len + num.len;

    for (int i = 0; i < len; i++)
        for (int j = 0; j < num.len; j++) result.s[i + j] += s[i] * num.s[j];

    for (int i = 0; i < result.len; i++) {
        result.s[i + 1] += result.s[i] / 10;
        result.s[i] %= 10;
    }
    result.clean();
    result.sign = !(sign ^ num.sign);
    return result;
}
bign bign::operator*(const int num) const {
    bign x = num;
    bign z = *this;
    return x * z;
}
bign bign::operator*=(const bign &num) {
    *this = *this * num;
    return *this;
}
bign bign::operator/(const bign &num) const {
    bign ans;
    ans.len = len - num.len + 1;
    if (ans.len < 0) {
        ans.len = 1;
        return ans;
    }

    bign divisor = *this, divid = num;
    divisor.sign = divid.sign = 1;
    int k = ans.len - 1;
    int j = len - 1;
    while (k >= 0) {
        while (divisor.s[j] == 0) j--;
        if (k > j)
            k = j;
        char z[MAX_L];
        memset(z, 0, sizeof(z));
        for (int i = j; i >= k; i--) z[j - i] = divisor.s[i] + '0';
        bign dividend = z;
        if (dividend < divid) {
            k--;
            continue;
        }
        int key = 0;
        while (divid * key <= dividend) key++;
        key--;
        ans.s[k] = key;
        bign temp = divid * key;
        for (int i = 0; i < k; i++) temp = temp * 10;
        divisor = divisor - temp;
        k--;
    }
    ans.clean();
    ans.sign = !(sign ^ num.sign);
    return ans;
}
bign bign::operator/=(const bign &num) {
    *this = *this / num;
    return *this;
}
bign bign::operator%(const bign &num) const {
    bign a = *this, b = num;
    a.sign = b.sign = 1;
    bign result, temp = a / b * b;
    result = a - temp;
    result.sign = sign;
    return result;
}
bign bign::pow(const bign &num) const {
    bign result = 1;
    for (bign i = 0; i < num; i++) result = result * (*this);
    return result;
}
bign bign::factorial() const {
    bign result = 1;
    for (bign i = 1; i <= *this; i++) result *= i;
    return result;
}
void bign::clean() {
    if (len == 0)
        len++;
    while (len > 1 && s[len - 1] == '\0') len--;
}
bign bign::Sqrt() const {
    if (*this < 0)
        return -1;
    if (*this <= 1)
        return *this;
    bign l = 0, r = *this, mid;
    while (r - l > 1) {
        mid = (l + r) / 2;
        if (mid * mid > *this)
            r = mid;
        else
            l = mid;
    }
    return l;
}
bign::~bign() {}

inline bign quickmi(ll xx, ll n) {
    bign x = xx, res = 1;
    for (; n; n >>= 1) {
        if (n & 1)
            res *= x;
        x *= x;
    }
    return res;
}