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 { static int M; import std.conv : to; uint x; this(ModInt a) { x = a.x; } this(uint x_) { x = x_ % M; } this(ulong x_) { x = cast(uint)(x_ % M); } this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; } this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); } ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); } ref ModInt opOpAssign(string op, T)(T a) { static if (is(T == ModInt)) { static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; } else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; } else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } else static if (op == "^^") { if (a < 0) return this = inv()^^(-a); ModInt b = this, c = 1U; for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; } return this = c; } else { return mixin("this " ~ op ~ "= ModInt(a)"); } } ModInt inv() const { uint a = M, b = x; int y = 0, z = 1; for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; } assert(a == 1); return ModInt(y); } ModInt opUnary(string op)() const { static if (op == "+") { return this; } else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; } else static assert(false); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0U); } string toString() const { return x.to!string; } } alias Mint = ModInt; Mint solve(int p, int e, long L, long R) { const m = p^^e; Mint.M = m; auto fac = new Mint[m]; fac[0] = 1; foreach (i; 1 .. m) { fac[i] = fac[i - 1] * ((i % p != 0) ? i : 1); } auto invFac = new Mint[m]; invFac[m - 1] = fac[m - 1].inv; foreach_reverse (i; 1 .. m) { invFac[i - 1] = invFac[i] * ((i % p != 0) ? i : 1); } Mint binom(long n, long k) { const l = n - k; Mint ret = 1; long sum1, sumE; int f; for (long nn = n, kk = k, ll = l; nn > 0; nn /= p, kk /= p, ll /= p, ++f) { ret *= fac[nn % m] * invFac[kk % m] * invFac[ll % m]; if (f >= 1) sum1 += (nn - kk - ll); if (f >= e) sumE += (nn - kk - ll); } if (!(p == 2 && e >= 3) && (sum1 & 1)) { ret = -ret; } ret *= p^^(min(sumE, e)); return ret; } Mint ret; foreach (n; L .. R + 1) { const res = binom(2 * n, n); debug { if (R - L <= 10) { writefln("binom(%s, %s) == %s (mod %s^%s)", 2 * n, n, res, p, e); } } ret += (res - 2); } return ret; } void main() { try { for (; ; ) { const L = readLong; const R = readLong; const M = readInt; int n = 1; int ans; void doIt(int p, int e) { const res = solve(p, e, L, R); for (; Mint(ans) != res; ans += n) {} n *= Mint.M; } { int m = M; for (int p = 2; p * p <= m; ++p) if (m % p == 0) { int e; do { ++e; m /= p; } while (m % p == 0); doIt(p, e); } if (m > 1) { doIt(m, 1); } } writeln(ans); } } catch (EOFException e) { } }