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- #include <bits/stdc++.h>
- using namespace std;
- #define popCnt(x) (__builtin_popcountll(x))
- typedef long long Long;
- // base and base_digits must be consistent
- const int base = 1000000000;
- const int base_digits = 9;
- struct BigInt {
- vector<int> z;
- int sign;
- BigInt() :
- sign(1) {
- }
- BigInt(long long v) {
- *this = v;
- }
- BigInt(const string &s) {
- read(s);
- }
- BigInt operator=(const BigInt &v) {
- sign = v.sign;
- z = v.z;
- return *this;
- }
- void operator=(long long v) {
- sign = 1;
- if (v < 0) sign = -1, v = -v;
- z.clear();
- for (; v > 0; v = v / base)
- z.push_back(v % base);
- }
- BigInt operator+(const BigInt &v) const {
- if (sign == v.sign) {
- BigInt res = v;
- for (int i = 0, carry = 0; i < (int) max(z.size(), v.z.size()) || carry;
- ++i) {
- if (i == (int) res.z.size()) res.z.push_back(0);
- res.z[i] += carry + (i < (int) z.size() ? z[i] : 0);
- carry = res.z[i] >= base;
- if (carry) res.z[i] -= base;
- }
- return res;
- }
- return *this - (-v);
- }
- BigInt operator-(const BigInt &v) const {
- if (sign == v.sign) {
- if (abs() >= v.abs()) {
- BigInt res = *this;
- for (int i = 0, carry = 0; i < (int) v.z.size() || carry; ++i) {
- res.z[i] -= carry + (i < (int) v.z.size() ? v.z[i] : 0);
- carry = res.z[i] < 0;
- if (carry) res.z[i] += base;
- }
- res.trim();
- return res;
- }
- return -(v - *this);
- }
- return *this + (-v);
- }
- void operator*=(int v) {
- if (v < 0) sign = -sign, v = -v;
- for (int i = 0, carry = 0; i < (int) z.size() || carry; ++i) {
- if (i == (int) z.size()) z.push_back(0);
- long long cur = z[i] * (long long) v + carry;
- carry = (int) (cur / base);
- z[i] = (int) (cur % base);
- //asm("divl %%ecx" : "=a"(carry), "=d"(a[i]) : "A"(cur), "c"(base));
- }
- trim();
- }
- BigInt operator*(int v) const {
- BigInt res = *this;
- res *= v;
- return res;
- }
- friend pair<BigInt, BigInt> divmod(const BigInt &a1, const BigInt &b1) {
- int norm = base / (b1.z.back() + 1);
- BigInt a = a1.abs() * norm;
- BigInt b = b1.abs() * norm;
- BigInt q, r;
- q.z.resize(a.z.size());
- for (int i = a.z.size() - 1; i >= 0; i--) {
- r *= base;
- r += a.z[i];
- int s1 = b.z.size() < r.z.size() ? r.z[b.z.size()] : 0;
- int s2 = b.z.size() - 1 < r.z.size() ? r.z[b.z.size() - 1] : 0;
- int d = ((long long) s1 * base + s2) / b.z.back();
- r -= b * d;
- while (r < 0)
- r += b, --d;
- q.z[i] = d;
- }
- q.sign = a1.sign * b1.sign;
- r.sign = a1.sign;
- q.trim();
- r.trim();
- return make_pair(q, r / norm);
- }
- friend BigInt sqrt(const BigInt &a1) {
- BigInt a = a1;
- while (a.z.empty() || a.z.size() % 2 == 1)
- a.z.push_back(0);
- int n = a.z.size();
- int firstDigit = (int) sqrt((double) a.z[n - 1] * base + a.z[n - 2]);
- int norm = base / (firstDigit + 1);
- a *= norm;
- a *= norm;
- while (a.z.empty() || a.z.size() % 2 == 1)
- a.z.push_back(0);
- BigInt r = (long long) a.z[n - 1] * base + a.z[n - 2];
- firstDigit = (int) sqrt((double) a.z[n - 1] * base + a.z[n - 2]);
- int q = firstDigit;
- BigInt res;
- for (int j = n / 2 - 1; j >= 0; j--) {
- for (;; --q) {
- BigInt r1 = (r - (res * 2 * base + q) * q) * base * base
- + (j > 0 ? (long long) a.z[2 * j - 1] * base + a.z[2 * j - 2] : 0);
- if (r1 >= 0) {
- r = r1;
- break;
- }
- }
- res *= base;
- res += q;
- if (j > 0) {
- int d1 = res.z.size() + 2 < r.z.size() ? r.z[res.z.size() + 2] : 0;
- int d2 = res.z.size() + 1 < r.z.size() ? r.z[res.z.size() + 1] : 0;
- int d3 = res.z.size() < r.z.size() ? r.z[res.z.size()] : 0;
- q = ((long long) d1 * base * base + (long long) d2 * base + d3)
- / (firstDigit * 2);
- }
- }
- res.trim();
- return res / norm;
- }
- BigInt operator/(const BigInt &v) const {
- return divmod(*this, v).first;
- }
- BigInt operator%(const BigInt &v) const {
- return divmod(*this, v).second;
- }
- void operator/=(int v) {
- if (v < 0) sign = -sign, v = -v;
- for (int i = (int) z.size() - 1, rem = 0; i >= 0; --i) {
- long long cur = z[i] + rem * (long long) base;
- z[i] = (int) (cur / v);
- rem = (int) (cur % v);
- }
- trim();
- }
- BigInt operator/(int v) const {
- BigInt res = *this;
- res /= v;
- return res;
- }
- int operator%(int v) const {
- if (v < 0) v = -v;
- int m = 0;
- for (int i = z.size() - 1; i >= 0; --i)
- m = (z[i] + m * (long long) base) % v;
- return m * sign;
- }
- void operator+=(const BigInt &v) {
- *this = *this + v;
- }
- void operator-=(const BigInt &v) {
- *this = *this - v;
- }
- void operator*=(const BigInt &v) {
- *this = *this * v;
- }
- void operator/=(const BigInt &v) {
- *this = *this / v;
- }
- bool operator<(const BigInt &v) const {
- if (sign != v.sign) return sign < v.sign;
- if (z.size() != v.z.size()) return z.size() * sign < v.z.size() * v.sign;
- for (int i = z.size() - 1; i >= 0; i--)
- if (z[i] != v.z[i]) return z[i] * sign < v.z[i] * sign;
- return false;
- }
- bool operator>(const BigInt &v) const {
- return v < *this;
- }
- bool operator<=(const BigInt &v) const {
- return !(v < *this);
- }
- bool operator>=(const BigInt &v) const {
- return !(*this < v);
- }
- bool operator==(const BigInt &v) const {
- return !(*this < v) && !(v < *this);
- }
- bool operator!=(const BigInt &v) const {
- return *this < v || v < *this;
- }
- void trim() {
- while (!z.empty() && z.back() == 0)
- z.pop_back();
- if (z.empty()) sign = 1;
- }
- bool isZero() const {
- return z.empty() || (z.size() == 1 && !z[0]);
- }
- BigInt operator-() const {
- BigInt res = *this;
- res.sign = -sign;
- return res;
- }
- BigInt abs() const {
- BigInt res = *this;
- res.sign *= res.sign;
- return res;
- }
- long long longValue() const {
- long long res = 0;
- for (int i = z.size() - 1; i >= 0; i--)
- res = res * base + z[i];
- return res * sign;
- }
- friend BigInt gcd(const BigInt &a, const BigInt &b) {
- return b.isZero() ? a : gcd(b, a % b);
- }
- friend BigInt lcm(const BigInt &a, const BigInt &b) {
- return a / gcd(a, b) * b;
- }
- void read(const string &s) {
- sign = 1;
- z.clear();
- int pos = 0;
- while (pos < (int) s.size() && (s[pos] == '-' || s[pos] == '+')) {
- if (s[pos] == '-') sign = -sign;
- ++pos;
- }
- for (int i = s.size() - 1; i >= pos; i -= base_digits) {
- int x = 0;
- for (int j = max(pos, i - base_digits + 1); j <= i; j++)
- x = x * 10 + s[j] - '0';
- z.push_back(x);
- }
- trim();
- }
- friend istream& operator>>(istream &stream, BigInt &v) {
- string s;
- stream >> s;
- v.read(s);
- return stream;
- }
- friend ostream& operator<<(ostream &stream, const BigInt &v) {
- if (v.sign == -1) stream << '-';
- stream << (v.z.empty() ? 0 : v.z.back());
- for (int i = (int) v.z.size() - 2; i >= 0; --i)
- stream << setw(base_digits) << setfill('0') << v.z[i];
- return stream;
- }
- static vector<int> convert_base(const vector<int> &a, int old_digits,
- int new_digits) {
- vector<long long> p(max(old_digits, new_digits) + 1);
- p[0] = 1;
- for (int i = 1; i < (int) p.size(); i++)
- p[i] = p[i - 1] * 10;
- vector<int> res;
- long long cur = 0;
- int cur_digits = 0;
- for (int i = 0; i < (int) a.size(); i++) {
- cur += a[i] * p[cur_digits];
- cur_digits += old_digits;
- while (cur_digits >= new_digits) {
- res.push_back(int(cur % p[new_digits]));
- cur /= p[new_digits];
- cur_digits -= new_digits;
- }
- }
- res.push_back((int) cur);
- while (!res.empty() && res.back() == 0)
- res.pop_back();
- return res;
- }
- typedef vector<long long> vll;
- static vll karatsubaMultiply(const vll &a, const vll &b) {
- int n = a.size();
- vll res(n + n);
- if (n <= 32) {
- for (int i = 0; i < n; i++)
- for (int j = 0; j < n; j++)
- res[i + j] += a[i] * b[j];
- return res;
- }
- int k = n >> 1;
- vll a1(a.begin(), a.begin() + k);
- vll a2(a.begin() + k, a.end());
- vll b1(b.begin(), b.begin() + k);
- vll b2(b.begin() + k, b.end());
- vll a1b1 = karatsubaMultiply(a1, b1);
- vll a2b2 = karatsubaMultiply(a2, b2);
- for (int i = 0; i < k; i++)
- a2[i] += a1[i];
- for (int i = 0; i < k; i++)
- b2[i] += b1[i];
- vll r = karatsubaMultiply(a2, b2);
- for (int i = 0; i < (int) a1b1.size(); i++)
- r[i] -= a1b1[i];
- for (int i = 0; i < (int) a2b2.size(); i++)
- r[i] -= a2b2[i];
- for (int i = 0; i < (int) r.size(); i++)
- res[i + k] += r[i];
- for (int i = 0; i < (int) a1b1.size(); i++)
- res[i] += a1b1[i];
- for (int i = 0; i < (int) a2b2.size(); i++)
- res[i + n] += a2b2[i];
- return res;
- }
- BigInt operator*(const BigInt &v) const {
- vector<int> a6 = convert_base(this->z, base_digits, 6);
- vector<int> b6 = convert_base(v.z, base_digits, 6);
- vll a(a6.begin(), a6.end());
- vll b(b6.begin(), b6.end());
- while (a.size() < b.size())
- a.push_back(0);
- while (b.size() < a.size())
- b.push_back(0);
- while (a.size() & (a.size() - 1))
- a.push_back(0), b.push_back(0);
- vll c = karatsubaMultiply(a, b);
- BigInt res;
- res.sign = sign * v.sign;
- for (int i = 0, carry = 0; i < (int) c.size(); i++) {
- long long cur = c[i] + carry;
- res.z.push_back((int) (cur % 1000000));
- carry = (int) (cur / 1000000);
- }
- res.z = convert_base(res.z, 6, base_digits);
- res.trim();
- return res;
- }
- };
- const int MX = 102;
- BigInt dp[MX][MX];
- BigInt ncr[MX][MX];
- BigInt C(int n, int r) {
- if (r < 0 || n < r || r > n) return 0;
- if (r == 0) return 1;
- auto& res = ncr[n][r];
- if (res != -1) return res;
- res = C(n - 1, r - 1) + C(n - 1, r);
- return res;
- }
- BigInt fact[MX];
- BigInt solve(int n, int k) {
- if (k < 0) return 0;
- if (n == 0) return k == 0;
- auto& res = dp[n][k];
- if (res != -1) return res;
- res = solve(n - 1, k - 1);
- for (int i = 2; i <= n; ++i) {
- res += solve(n - i, k) * C(n - 1, i - 1) * fact[i - 1];
- }
- return res;
- }
- int main() {
- fact[0] = 1;
- for (int i = 1; i < MX; ++i) {
- fact[i] = fact[i - 1] * i;
- }
- for (int i = 0; i < MX; ++i) {
- for (int j = 0; j < MX; ++j) {
- ncr[i][j] = -1;
- dp[i][j] = -1;
- }
- }
- int n, k;
- cin >> k >> n;
- auto x = solve(n, k);
- auto y = fact[n];
- if (x == 0) {
- cout << 0;
- return 0;
- }
- auto g = gcd(x, y);
- x /= g;
- y /= g;
- cout << x << "/" << y;
- }
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