# competitive-programming-library

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# modulus/twelvefold_way.balls_and_boxes_3.test.cpp

## Code

#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_C"
#include <iostream>
#include "modulus/twelvefold_way.hpp"
using namespace std;

constexpr int MOD = 1e9 + 7;
int main() {
int n, k; cin >> n >> k;
cout << twelvefold_lls<MOD>(n, k) << endl;
return 0;
}



#line 1 "modulus/twelvefold_way.balls_and_boxes_3.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_C"
#include <iostream>
#line 2 "modulus/mint.hpp"
#include <cstdint>
#line 2 "modulus/modpow.hpp"
#include <cassert>
#line 4 "modulus/modpow.hpp"

inline int32_t modpow(uint_fast64_t x, uint64_t k, int32_t MOD) {
assert (/* 0 <= x and */ x < (uint_fast64_t)MOD);
uint_fast64_t y = 1;
for (; k; k >>= 1) {
if (k & 1) (y *= x) %= MOD;
(x *= x) %= MOD;
}
assert (/* 0 <= y and */ y < (uint_fast64_t)MOD);
return y;
}
#line 2 "modulus/modinv.hpp"
#include <algorithm>
#line 5 "modulus/modinv.hpp"

inline int32_t modinv_nocheck(int32_t value, int32_t MOD) {
assert (0 <= value and value < MOD);
if (value == 0) return -1;
int64_t a = value, b = MOD;
int64_t x = 0, y = 1;
for (int64_t u = 1, v = 0; a; ) {
int64_t q = b / a;
x -= q * u; std::swap(x, u);
y -= q * v; std::swap(y, v);
b -= q * a; std::swap(b, a);
}
if (not (value * x + MOD * y == b and b == 1)) return -1;
if (x < 0) x += MOD;
assert (0 <= x and x < MOD);
return x;
}

inline int32_t modinv(int32_t x, int32_t MOD) {
int32_t y = modinv_nocheck(x, MOD);
assert (y != -1);
return y;
}
#line 6 "modulus/mint.hpp"

/**
* @brief quotient ring / 剰余環 $\mathbb{Z}/n\mathbb{Z}$
*/
template <int32_t MOD>
struct mint {
int32_t value;
mint() : value() {}
mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {}
mint(int32_t value_, std::nullptr_t) : value(value_) {}
explicit operator bool() const { return value; }
inline mint<MOD> operator + (mint<MOD> other) const { return mint<MOD>(*this) += other; }
inline mint<MOD> operator - (mint<MOD> other) const { return mint<MOD>(*this) -= other; }
inline mint<MOD> operator * (mint<MOD> other) const { return mint<MOD>(*this) *= other; }
inline mint<MOD> & operator += (mint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; }
inline mint<MOD> & operator -= (mint<MOD> other) { this->value -= other.value; if (this->value <    0) this->value += MOD; return *this; }
inline mint<MOD> & operator *= (mint<MOD> other) { this->value = (uint_fast64_t)this->value * other.value % MOD; return *this; }
inline mint<MOD> operator - () const { return mint<MOD>(this->value ? MOD - this->value : 0, nullptr); }
inline bool operator == (mint<MOD> other) const { return value == other.value; }
inline bool operator != (mint<MOD> other) const { return value != other.value; }
inline mint<MOD> pow(uint64_t k) const { return mint<MOD>(modpow(value, k, MOD), nullptr); }
inline mint<MOD> inv() const { return mint<MOD>(modinv(value, MOD), nullptr); }
inline mint<MOD> operator / (mint<MOD> other) const { return *this * other.inv(); }
inline mint<MOD> & operator /= (mint<MOD> other) { return *this *= other.inv(); }
};
template <int32_t MOD> mint<MOD> operator + (int64_t value, mint<MOD> n) { return mint<MOD>(value) + n; }
template <int32_t MOD> mint<MOD> operator - (int64_t value, mint<MOD> n) { return mint<MOD>(value) - n; }
template <int32_t MOD> mint<MOD> operator * (int64_t value, mint<MOD> n) { return mint<MOD>(value) * n; }
template <int32_t MOD> mint<MOD> operator / (int64_t value, mint<MOD> n) { return mint<MOD>(value) / n; }
template <int32_t MOD> std::istream & operator >> (std::istream & in, mint<MOD> & n) { int64_t value; in >> value; n = value; return in; }
template <int32_t MOD> std::ostream & operator << (std::ostream & out, mint<MOD> n) { return out << n.value; }
#line 2 "modulus/factorial.hpp"
#include <vector>
#line 4 "modulus/factorial.hpp"

template <int32_t MOD>
mint<MOD> fact(int n) {
static std::vector<mint<MOD> > memo(1, 1);
while (n >= memo.size()) {
memo.push_back(memo.back() * mint<MOD>(memo.size()));
}
return memo[n];
}
template <int32_t MOD>
mint<MOD> inv_fact(int n) {
static std::vector<mint<MOD> > memo;
if (memo.size() <= n) {
int l = memo.size();
int r = n * 1.3 + 100;
memo.resize(r);
memo[r - 1] = fact<MOD>(r - 1).inv();
for (int i = r - 2; i >= l; -- i) {
memo[i] = memo[i + 1] * (i + 1);
}
}
return memo[n];
}
#line 5 "modulus/choose.hpp"

/**
* @brief combination / 組合せ ${} _ n C _ r$ (前処理 $O(n)$ + $O(1)$)
*/
template <int32_t MOD>
mint<MOD> choose(int n, int r) {
assert (0 <= r and r <= n);
return fact<MOD>(n) * inv_fact<MOD>(n - r) * inv_fact<MOD>(r);
}
#line 5 "modulus/permute.hpp"

/**
* @brief permutation / 順列 ${} _ n P _ r$ (前処理 $O(n)$ + $O(1)$)
*/
template <int32_t MOD>
mint<MOD> permute(int n, int r) {
assert (0 <= r and r <= n);
return fact<MOD>(n) * inv_fact<MOD>(n - r);
}
#line 5 "modulus/multichoose.hpp"

/**
* @brief 重複組合せ ${} _ n H _ r = {} _ {n + r - 1} C _ r$ (前処理 $O(n)$ + $O(1)$)
*/
template <int32_t MOD>
mint<MOD> multichoose(int n, int r) {
assert (0 <= n and 0 <= r);
if (n == 0 and r == 0) return 1;
return choose<MOD>(n + r - 1, r);
}
#line 4 "modulus/stirling_number_of_the_second_kind_direct.hpp"
#include <map>
#line 2 "utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 9 "modulus/stirling_number_of_the_second_kind_direct.hpp"

/**
* @brief the Stirling number of the second kind ($O(K \log N)$)
*/
template <int MOD>
mint<MOD> stirling_number_of_the_second_kind_direct(int n, int k) {
assert (0 <= n and 0 <= k);
mint<MOD> acc = 0;
REP (i, k + 1) {
int parity = ((k - i) % 2 == 0 ? +1 : -1);
acc += choose<MOD>(k, i) * mint<MOD>(i).pow(n) * parity;
}
return acc * inv_fact<MOD>(k);
}
#line 6 "modulus/stirling_number_of_the_second_kind_table.hpp"

/**
* @brief the Stirling number of the second kind (前処理 $O(NK)$ + $O(1)$)
* @description the number of ways of partitioning a set of n elements into k nonempty sets
* @see http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html
* @see http://oeis.org/A008277
* @see https://ja.wikipedia.org/wiki/%E3%82%B9%E3%82%BF%E3%83%BC%E3%83%AA%E3%83%B3%E3%82%B0%E6%95%B0#.E7.AC.AC2.E7.A8.AE.E3.82.B9.E3.82.BF.E3.83.BC.E3.83.AA.E3.83.B3.E3.82.B0.E6.95.B0
*/
template <int MOD>
mint<MOD> stirling_number_of_the_second_kind_table(int n, int k) {
assert (0 <= n and 0 <= k);
if (n  < k) return 0;
if (n == k) return 1;
if (k == 0) return 0;
static std::vector<std::vector<mint<MOD> > > memo;
if (memo.size() <= n) {
int l = memo.size();
memo.resize(n + 1);
REP3 (i, l, n + 1) {
memo[i].resize(i);
}
}
if (memo[n][k]) return memo[n][k];
return memo[n][k] =
stirling_number_of_the_second_kind_table<MOD>(n - 1, k - 1) +
stirling_number_of_the_second_kind_table<MOD>(n - 1, k) * k;
}
#line 5 "modulus/bell_number.hpp"

/**
* @brief the Bell number (前処理 $O(NK)$ + $O(1)$)
* @description the number of ways a set of n elements can be partitioned into nonempty subsets
* @see http://mathworld.wolfram.com/BellNumber.html
* @see https://oeis.org/A110
* @see https://ja.wikipedia.org/wiki/%E3%83%99%E3%83%AB%E6%95%B0
*/
template <int PRIME>
mint<PRIME> bell_number(int n, int k) {
static std::vector<std::vector<mint<PRIME> > > memo;
if (memo.size() <= n) {
memo.resize(n + 1);
}
if (memo[n].empty()) {
memo[n].push_back(0);
}
while (memo[n].size() <= k) {
int i = memo[n].size();
memo[n].push_back(memo[n].back() + stirling_number_of_the_second_kind_table<PRIME>(n, i));
}
return memo[n][k];
}

template <int PRIME>
mint<PRIME> unary_bell_number(int n) {
return bell_number<PRIME>(n, n);
}
#line 5 "modulus/partition_number.hpp"

/**
* @brief the partition number (前処理 $O(NK)$ + $O(1)$)
* @description the number of non-decreasing sequences with the length k which the sum is n
*/
template <int MOD>
mint<MOD> partition_number(int n, int k) {
static std::vector<std::vector<mint<MOD> > > memo;
if (memo.size() <= n) {
memo.resize(n + 1);
}
while (memo[n].size() <= k) {
if (n == 0) {
memo[0].resize(k + 1, 1);
} else if (memo[n].empty()) {
memo[n].push_back(0);
} else {
int j = memo[n].size();
auto a = (n - j >= 0 ? partition_number<MOD>(n - j, j) : 0);
auto b = (j - 1 >= 0 ? partition_number<MOD>(n, j - 1) : 0);
memo[n].push_back(a + b);
}
}
return memo[n][k];
}

template <int MOD>
mint<MOD> unary_partition_number(int n) {
return partition_number<MOD>(n, n);
}

#line 9 "modulus/twelvefold_way.hpp"

/**
* @brief twelvefold way / 写像12相
* @sa https://en.wikipedia.org/wiki/Twelvefold_way
* @sa https://mathtrain.jp/twelveway
* @note the numbers of mapprings f putting N balls into K boxes
*/

/**
* @brief labeled-N labeled-K any-f
* @note the number of f for all f : N \to K
* @note O(log K)
*/
template <int MOD>
mint<MOD> twelvefold_lla(int n, int k) {
return mint<MOD>(k).pow(n);
}

/**
* @brief labeled-N labeled-K injective-f
* @note the number of f for injective f : N \rightarrowtail K
* @note O(1) with precomputation O(N + K)
*/
template <int MOD>
mint<MOD> twelvefold_lli(int n, int k) {
if (n > k) return 0;
return permute<MOD>(k, n);
}

/**
* @brief labeled-N labeled-K surjective-f
* @note the number of f for surjective f : N \twoheadrightarrow K
* @note O(NK) or O(N \log K)
*/
template <int MOD>
mint<MOD> twelvefold_lls(int n, int k) {
return stirling_number_of_the_second_kind_direct<MOD>(n, k) * fact<MOD>(k);
}

/**
* @brief unlabeled-N labeled-K any-f
* @note the number of f \circ S_N for any f : N \to K
* @note O(1) with precomputation O(N + K)
*/
template <int MOD>
mint<MOD> twelvefold_ula(int n, int k) {
return choose<MOD>(n + k - 1, n);
}

/**
* @brief unlabeled-N labeled-K injective-f
* @note the number of f \circ S_N for injective f : N \rightarrowtail K
* @note O(1) with precomputation O(K)
*/
template <int MOD>
mint<MOD> twelvefold_uli(int n, int k) {
if (n > k) return 0;
return choose<MOD>(k, n);
}

/**
* @brief unlabeled-N labeled-K surjective-f
* @note the number of f \circ S_N for surjective f : N \twoheadrightarrow K
* @note O(1) with precomputation O(N)
*/
template <int MOD>
mint<MOD> twelvefold_uls(int n, int k) {
if (n < k) return 0;
return choose<MOD>(n - 1, n - k);
}

/**
* @brief labeled-N unlabeled-K any-f
* @note the number of S_K \circ f for all f : N \to K
*/
template <int MOD>
mint<MOD> twelvefold_lua(int n, int k) {
return bell_number<MOD>(n, k);
}

/**
* @brief labeled-N unlabeled-K injective-f
* @note the number of S_K \circ f for injective f : N \rightarrowtail K
* @note O(1)
*/
template <int MOD>
mint<MOD> twelvefold_lui(int n, int k) {
if (n > k) return 0;
return 1;
}

/**
* @brief labeled-N unlabeled-K surjective-f
* @note the number of S_K \circ f for surjective f : N \twoheadrightarrow K
* @note O(NK) or O(N \log K)
*/
template <int MOD>
mint<MOD> twelvefold_lus(int n, int k) {
return stirling_number_of_the_second_kind_direct<MOD>(n, k);
}

/**
* @brief unlabeled-N unlabeled-K any-f
*/
template <int MOD>
mint<MOD> twelvefold_uua(int n, int k) {
return partition_number<MOD>(n, k);
}

/**
* @brief unlabeled-N unlabeled-K injective-f
* @note the number of S_K \circ f \circ S_N for injective f : N \rightarrowtail K
* @note O(1)
*/
template <int MOD>
mint<MOD> twelvefold_uui(int n, int k) {
if (n > k) return 0;
return 1;
}
#line 4 "modulus/twelvefold_way.balls_and_boxes_3.test.cpp"
using namespace std;

constexpr int MOD = 1e9 + 7;
int main() {
int n, k; cin >> n >> k;
cout << twelvefold_lls<MOD>(n, k) << endl;
return 0;
}