#include "bits/stdc++.h" using namespace std; #ifdef _DEBUG #include "dump.hpp" #else #define dump(...) #endif //#define int long long #define rep(i,a,b) for(int i=(a);i<(b);i++) #define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--) #define all(c) begin(c),end(c) const int INF = sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f; const int MOD = 1'000'000'007; template bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T &a, const T &b) { if (b < a) { a = b; return true; } return false; } template struct ModInt { static const int kMod = MOD; unsigned x; ModInt() : x(0) {} ModInt(signed sig) { int sigt = sig % kMod; if (sigt < 0) sigt += kMod; x = sigt; } ModInt(signed long long sig) { int sigt = sig % kMod; if (sigt < 0) sigt += kMod; x = sigt; } int get() const { return (int)x; } ModInt &operator+=(ModInt that) { if ((x += that.x) >= kMod) x -= kMod; return *this; } ModInt &operator-=(ModInt that) { if ((x += kMod - that.x) >= kMod) x -= kMod; return *this; } ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % kMod; return *this; } ModInt &operator/=(ModInt that) { return *this *= that.inverse(); } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } ModInt inverse() const { signed a = x, b = kMod, u = 1, v = 0; while (b) { signed t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if (u < 0) u += kMod; ModInt res; res.x = (unsigned)u; return res; } }; template ostream &operator << (ostream &os, const ModInt &m) { return os << m.x; } template istream &operator >> (istream &is, ModInt &m) { signed long long s; is >> s; m = ModInt(s); return is; }; using mint = ModInt<1000000007>; mint pow(mint a, unsigned long long k) { mint r = 1; while (k) { if (k & 1) r *= a; a *= a; k >>= 1; } return r; } vector fact, factinv; void precomputeFactorial(int N) { N = min(N, mint::kMod - 1); fact.resize(N + 1); factinv.resize(N + 1); fact[0] = 1; rep(i, 1, N + 1) fact[i] = fact[i - 1] * i; factinv[N] = fact[N].inverse(); for (int i = N; i >= 1; i--) factinv[i - 1] = factinv[i] * i; } mint combi(int n, int r) { if (n >= mint::kMod) return combi(n % mint::kMod, r % mint::kMod) * combi(n / mint::kMod, r / mint::kMod); return r > n ? 0 : fact[n] * factinv[n - r] * factinv[r]; } signed main() { cin.tie(0); ios::sync_with_stdio(false); int N, M, K; cin >> N >> M >> K; vector L(M), R(M); rep(i, 0, M) { cin >> L[i] >> R[i]; L[i], R[i]; L[i]--; } vector> dp(K + 1, vector(N)); dp[0][0] = 1; rep(k, 0, K) { vector sum(N + 1); rep(i, 0, N) { sum[i + 1] += sum[i] + dp[k][i]; } vector imos(N + 1); rep(i, 0, M) { mint add = sum[R[i]] - sum[L[i]]; imos[L[i]] += add; imos[R[i]] -= add; } rep(i, 0, N) { imos[i + 1] += imos[i]; } rep(i, 0, N) { dp[k + 1][i] = imos[i]; } } cout << dp[K][N - 1] << endl; return 0; }