test/aoj_DPL_5_L.test.cpp

#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_L"

#include <cstdio>
#include <vector>

#include "ModularArithmetic/modint.cpp"

using mi = modint<1000'000'007>;

int main() {
  size_t n, k;
  scanf("%zu %zu", &n, &k);

  if (n < k) return puts("0"), 0;

  std::vector<mi> dp(n+1, 0);
  dp[0] = 1;
  for (size_t i = 1; i <= k; ++i)
    for (size_t j = i; j <= n; ++j)
      dp[j] += dp[j-i];

  printf("%d\n", dp[n-k].get());
}

#line 1 "test/aoj_DPL_5_L.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_5_L"

#include <cstdio>
#include <vector>

#line 1 "ModularArithmetic/modint.cpp"



/**
 * @brief 合同算術用クラス
 * @author えびちゃん
 */

#include <cstdint>
#include <limits>
#include <type_traits>
#include <utility>

template <intmax_t Modulo>
class modint {
public:
  using value_type = typename std::conditional<
  (0 < Modulo && Modulo < std::numeric_limits<int>::max() / 2), int, intmax_t
 >::type;

private:
  static constexpr value_type S_cmod = Modulo;  // compile-time
  static value_type S_rmod;  // runtime
  value_type M_value = 0;

  static constexpr value_type S_inv(value_type n, value_type m) {
    value_type x = 0;
    value_type y = 1;
    value_type a = n;
    value_type b = m;
    for (value_type u = y, v = x; a;) {
      value_type q = b / a;
      std::swap(x -= q*u, u);
      std::swap(y -= q*v, v);
      std::swap(b -= q*a, a);
    }
    if ((x %= m) < 0) x += m;
    return x;
  }

  static value_type S_normalize(intmax_t n, value_type m) {
    if (n >= m) {
      n %= m;
    } else if (n < 0) {
      if ((n %= m) < 0) n += m;
    }
    return n;
  }

public:
  modint() = default;
  modint(intmax_t n): M_value(S_normalize(n, get_modulo())) {}

  modint& operator =(intmax_t n) {
    M_value = S_normalize(n, get_modulo());
    return *this;
  }

  modint& operator +=(modint const& that) {
    if ((M_value += that.M_value) >= get_modulo()) M_value -= get_modulo();
    return *this;
  }
  modint& operator -=(modint const& that) {
    if ((M_value -= that.M_value) < 0) M_value += get_modulo();
    return *this;
  }
  modint& operator *=(modint const& that) {
    intmax_t tmp = M_value;
    tmp *= that.M_value;
    M_value = tmp % get_modulo();
    return *this;
  }
  modint& operator /=(modint const& that) {
    intmax_t tmp = M_value;
    tmp *= S_inv(that.M_value, get_modulo());
    M_value = tmp % get_modulo();
    return *this;
  }

  modint& operator ++() {
    if (++M_value == get_modulo()) M_value = 0;
    return *this;
  }
  modint& operator --() {
    if (M_value-- == 0) M_value = get_modulo()-1;
    return *this;
  }

  modint operator ++(int) { modint tmp(*this); ++*this; return tmp; }
  modint operator --(int) { modint tmp(*this); --*this; return tmp; }

  friend modint operator +(modint lhs, modint const& rhs) { return lhs += rhs; }
  friend modint operator -(modint lhs, modint const& rhs) { return lhs -= rhs; }
  friend modint operator *(modint lhs, modint const& rhs) { return lhs *= rhs; }
  friend modint operator /(modint lhs, modint const& rhs) { return lhs /= rhs; }

  modint operator +() const { return *this; }
  modint operator -() const {
    if (M_value == 0) return *this;
    return modint(get_modulo() - M_value);
  }

  friend bool operator ==(modint const& lhs, modint const& rhs) {
    return lhs.M_value == rhs.M_value;
  }
  friend bool operator !=(modint const& lhs, modint const& rhs) {
    return !(lhs == rhs);
  }

  value_type get() const { return M_value; }
  static value_type get_modulo() { return ((S_cmod > 0)? S_cmod: S_rmod); }

  template <int M = Modulo, typename Tp = typename std::enable_if<(M <= 0)>::type>
  static Tp set_modulo(value_type m) { S_rmod = m; }
};

template <intmax_t N>
constexpr typename modint<N>::value_type modint<N>::S_cmod;
template <intmax_t N>
typename modint<N>::value_type modint<N>::S_rmod;


#line 7 "test/aoj_DPL_5_L.test.cpp"

using mi = modint<1000'000'007>;

int main() {
  size_t n, k;
  scanf("%zu %zu", &n, &k);

  if (n < k) return puts("0"), 0;

  std::vector<mi> dp(n+1, 0);
  dp[0] = 1;
  for (size_t i = 1; i <= k; ++i)
    for (size_t j = i; j <= n; ++j)
      dp[j] += dp[j-i];

  printf("%d\n", dp[n-k].get());
}