import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } struct ModInt(int M_) { import std.conv : to; alias M = M_; int x; this(ModInt a) { x = a.x; } this(long a) { x = cast(int)(a % M); if (x < 0) x += M; } ref ModInt opAssign(long a) { return (this = ModInt(a)); } ref ModInt opOpAssign(string op)(ModInt a) { static if (op == "+") { x += a.x; if (x >= M) x -= M; } else static if (op == "-") { x -= a.x; if (x < 0) x += M; } else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } ref ModInt opOpAssign(string op)(long a) { static if (op == "^^") { if (a < 0) return (this = inv()^^(-a)); ModInt t2 = this, te = ModInt(1); for (long e = a; e > 0; e >>= 1) { if (e & 1) te *= t2; t2 *= t2; } x = cast(int)(te.x); return this; } else return mixin("this " ~ op ~ "= ModInt(a)"); } ModInt inv() const { int a = x, b = M, y = 1, z = 0, t; for (; ; ) { t = a / b; a -= t * b; if (a == 0) { assert(b == 1 || b == -1); return ModInt(b * z); } y -= t * z; t = b / a; b -= t * a; if (b == 0) { assert(a == 1 || a == -1); return ModInt(a * y); } z -= t * y; } } ModInt opUnary(string op: "-")() const { return ModInt(-x); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op)(long a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0); } string toString() const { return x.to!string; } } enum MO = 10^^9 + 7; alias Mint = ModInt!MO; enum LIM = 110; Mint[] inv, fac, invFac; void prepare() { inv = new Mint[LIM]; fac = new Mint[LIM]; invFac = new Mint[LIM]; inv[1] = 1; foreach (i; 2 .. LIM) { inv[i] = -(Mint.M / i) * inv[cast(size_t)(Mint.M % i)]; } fac[0] = invFac[0] = 1; foreach (i; 1 .. LIM) { fac[i] = fac[i - 1] * i; invFac[i] = invFac[i - 1] * inv[i]; } } Mint binom(long n, long k) { if (0 <= k && k <= n) { assert(n < LIM); return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)]; } else { return Mint(0); } } void main() { prepare; try { for (; ; ) { const N = readInt(); const M = readInt(); const K = readInt(); auto A = new long[M]; auto B = new long[M]; foreach (i; 0 .. M) { A[i] = readLong(); B[i] = readLong(); } auto as = A.dup; as ~= 0; as ~= K + 1; as.sort; as = as.uniq.array; const asLen = cast(int)(as.length) - 1; auto bss = new long[][asLen]; foreach (i; 0 .. M) { const e = as.upperBound(A[i]) - 1; bss[e] ~= B[i]; } debug { writeln("as = ", as); writeln("bss = ", bss); } auto coef = new Mint[][](asLen, N + 1); auto coefGoal = new Mint[][](asLen, N + 1); foreach (e; 0 .. asLen) { foreach (dj; 0 .. N + 1) { coef[e][dj] = invFac[dj] * Mint(as[e + 1] - as[e])^^dj; coefGoal[e][dj] = invFac[dj] * Mint(K + 1 - as[e + 1])^^dj; } } Mint ans; foreach (b0; B) { debug { long counter; writeln("b0 = ", b0); } const numLarge = cast(int)(B.count!(b => (b > b0))); const numSmall = cast(int)(B.count!(b => (b < b0))); // processed poss, # of customers, stock (+, 0, -) auto dp = new Mint[][][][][](asLen + 1, N + 1, numLarge + 1, 2, numSmall + 1); dp[0][0][0][0][0] = 1; foreach (e; 0 .. asLen) { int dx, dy, dz; foreach (b; bss[e]) { if (b > b0) ++dx; if (b == b0) ++dy; if (b < b0) ++dz; } foreach (j; 0 .. N + 1) { foreach (x; 0 .. numLarge + 1) foreach (y; 0 .. 2) foreach (z; 0 .. numSmall + 1) { if (dp[e][j][x][y][z]) { int xx = x + dx, yy = y + dy, zz = z + dz; foreach (dj; 0 .. N - j + 1) { debug{ ++counter; } // dp[e + 1][j + dj][xx][yy][zz] += dp[e][j][x][y][z] * coef[e][dj]; if (y + dy > 0 && yy == 0) { // goal dp[asLen][N][0][0][0] += dp[e][j][x][y][z] * coef[e][dj] * coefGoal[e][N - (j + dj)]; } else { dp[e + 1][j + dj][xx][yy][zz] += dp[e][j][x][y][z] * coef[e][dj]; } (xx > 0) ? --xx : (yy > 0) ? --yy : (zz > 0) ? --zz : 0; } } } } } Mint sum; foreach (x; 0 .. numLarge + 1) foreach (z; 0 .. numSmall + 1) { sum += dp[asLen][N][x][0][z]; } sum *= fac[N]; debug { writeln("counter = ",counter); writeln(" sum = ", sum); stdout.flush; } ans += sum * b0; } ans /= Mint(K + 1)^^N; writeln(ans); } } catch (EOFException e) { } }