#include using namespace std; using i64 = int64_t; const i64 MOD = 1e9+7; const i64 INF = 1e18+7; // pythonのrangeのような範囲for文用のclass for(const auto& i : Range<>(10)) のように書く template struct Range{ struct iterator{ T value; const T step, last; const T& operator*(){return value;} iterator(T value, T step, T last) : value(value), step(step), last(last) { } iterator operator++(){value = step < static_cast(0) ? max(value + step, last) : min(value + step, last); return *this;} bool operator!=(const iterator& x){return value != x.value;} }; const T start, last, step; Range(const T start, const T last, const T step = static_cast(1)) : start(start), last(last), step(step) { } Range(const T last) : start(0), last(last), step(1) { } iterator begin(){return iterator(start, step, last);} iterator end(){return iterator(last, step, last);} }; // lambda式を用いた再帰 template struct FixPoint{ const F _f; FixPoint(F&& f) : _f(forward(f)){} template decltype(auto) operator()(Types&&... args) const{ return _f(*this, forward(args)...); } }; template static decltype(auto) makeRec(F&& f){ return FixPoint(forward(f)); } // 多次元vectorの一斉初期化 makeVector(a, b, ...)のように書く template vector makeVector(size_t x){ return vector(x, T(Value)); } template auto makeVector(size_t x, Types... args){ return vector(args...))>(x, makeVector(args...)); } // 最大値を更新し、更新できた時にはtrueを返す template bool chmax(T& a, T b){ if(a < b){ a = b; return true; } return false; } // 同様に最小値を更新する template bool chmin(T& a, T b){ if(a > b){ a = b; return true; } return false; } // 行数と変数名、値をclogに表示するデバッグ用print #define dump(x) fprintf(stderr, "line =%4d, name =%7s , ", __LINE__, #x); clog << "value = " << x << endl; // 同様の配列向けデバッグ用print #define vecdump(x) fprintf(stderr, "line =%4d, name =%7s\n", __LINE__, #x); _dump_macro(x); void _dump(int, string& x){ clog << x << endl; } template void _dump(bool, T& x){ clog << x << " "; } template void _dump(int, T& x){ for(auto& elm : x) _dump(0, elm); clog << endl; } template void _dump_macro(T& x){ _dump(0, x); } // input用の関数群 void _input(int, string& x){ cin >> x; } template void _input(bool, T& x){ cin >> x; } template void _input(int, T& x){ for(auto& elm : x) _input(0, elm); } template void input_single(T& x){ _input(0, x); } auto input(){} template void input(T& value, Types&&... args){ input_single(value); input(forward(args)...); }; void _pararell_input(size_t){} template void _pararell_input(size_t index, T& value, Types&&... args){ input(value[index]); _pararell_input(index, forward(args)...); } template void pararell_input(size_t count, Types&&... args){ for(const auto& i : Range<>(count)) _pararell_input(i, forward(args)...); } template struct Segtree{ int n; T op_t; U op_u; vector elm; vector lazy; vector length; function f; function g; function h; Segtree(int n, T init, function f, function g, function h, T op_t = T(), U op_u = U()) : n(n), op_t(op_t), op_u(op_u), elm(2 * n, init), lazy(2 * n, op_u), length(2 * n, 0), f(f), g(g), h(h) { for(int i = n - 1; i > 0; --i){ elm[i] = f(elm[2 * i], elm[2 * i + 1]); length[i] = length[2 * i] + 1; } } vector get_list(int x, int y){ vector ret_list; for(x += n, y += n - 1; x; x >>= 1, y >>= 1){ ret_list.emplace_back(x); if(x != y) ret_list.emplace_back(y); } return ret_list; } void eval(int x){ elm[x] = g(elm[x], lazy[x], 1 << length[x]); if(x < n){ lazy[2 * x] = h(lazy[2 * x], lazy[x]); lazy[2 * x + 1] = h(lazy[2 * x + 1], lazy[x]); } lazy[x] = op_u; } void update(int x, int y, U val){ vector index_list = get_list(x, y); for(int i = index_list.size() - 1; i >= 0; --i) eval(index_list[i]); for(x += n, y += n - 1; x <= y; x >>= 1, y >>= 1){ if(x & 1){ lazy[x] = h(lazy[x], val); eval(x++); } if(!(y & 1)){ lazy[y] = h(lazy[y], val); eval(y--); } } for(auto index : index_list){ if(index < n){ eval(2 * index); eval(2 * index + 1); elm[index] = f(elm[2 * index], elm[2 * index + 1]); } } } T get(int x, int y){ vector index_list = get_list(x, y); for(int i = index_list.size() - 1; i >= 0; --i) eval(index_list[i]); T val = op_t; for(x += n, y += n - 1; x <= y; x >>= 1, y >>= 1){ if(x & 1){ eval(x); val = f(val, elm[x++]); } if(!(y & 1)){ eval(y); val = f(val, elm[y--]); } } return val; } }; signed main(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); int n, m, k; input(n, m, k); vector> p; for(const auto& _ : Range<>(m)){ int x, y; input(x, y); p.emplace_back(--x, y); } Segtree dp(n, 0, [](i64 x, i64 y){return (x + y) % MOD;}, [](i64 x, i64 y, int z){return (x + y * z) % MOD;}, [](i64 x, i64 y){return (x + y) % MOD;}, 0, 0); dp.update(0, 1, 1); for(const auto& i : Range<>(k)){ Segtree nex(n, 0, [](i64 x, i64 y){return (x + y) % MOD;}, [](i64 x, i64 y, int z){return (x + y * z) % MOD;}, [](i64 x, i64 y){return (x + y) % MOD;}, 0, 0); for(auto& q : p){ auto [l, r] = q; auto val = dp.get(l, r); nex.update(l, r, val); } dp = move(nex); } cout << dp.get(n - 1, n) << endl; }