import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.complex, std.container, std.math, 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)); } // a^-1 (mod m) long modInv(long a, long m) in { assert(m > 0, "modInv: m > 0 must hold"); } do { long b = m, x = 1, y = 0, t; for (; ; ) { t = a / b; a -= t * b; if (a == 0) { assert(b == 1 || b == -1, "modInv: gcd(a, m) != 1"); if (b == -1) { y = -y; } return (y < 0) ? (y + m) : y; } x -= t * y; t = b / a; b -= t * a; if (b == 0) { assert(a == 1 || a == -1, "modInv: gcd(a, m) != 1"); if (a == -1) { x = -x; } return (x < 0) ? (x + m) : x; } y -= t * x; } } enum MO = 10L^^9 + 7; enum LIM = 10^^6; long[] inv, fac, invFac; void prepare() { inv = new long[LIM]; fac = new long[LIM]; invFac = new long[LIM]; inv[1] = 1; foreach (i; 2 .. LIM) { inv[i] = MO - ((MO / i) * inv[cast(size_t)(MO % i)]) % MO; } fac[0] = invFac[0] = 1; foreach (i; 1 .. LIM) { fac[i] = (fac[i - 1] * i) % MO; invFac[i] = (invFac[i - 1] * inv[i]) % MO; } } long binom(long n, long k) { if (0 <= k && k <= n) { assert(n < LIM); return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] % MO * invFac[cast(size_t)(n - k)] % MO; } else { return 0; } } long power(long a, long e) { long x = a % MO, y = 1; for (; e; e >>= 1) { if (e & 1) { y = (y * x) % MO; } x = (x * x) % MO; } return y; } long N; int K; void main() { prepare(); try { for (; ; ) { N = readLong(); K = readInt(); auto f = new long[K + 2]; f[0] = 0; foreach (i; 1 .. K + 2) { f[i] = (f[i - 1] + power(i, K)) % MO; } bool zero; long prod = 1; foreach (i; 0 .. K + 2) { const d = (N - i) % MO; if (d == 0) { zero = true; } else { prod *= d; prod %= MO; } } debug { writeln("zero = ", zero, ", prod = ", prod); } long ans; foreach (i; 0 .. K + 2) { const d = (N - i) % MO; long tmp = f[i]; if (zero) { tmp *= ((d == 0) ? prod : 0); tmp %= MO; } else { tmp *= prod; tmp %= MO; tmp *= modInv(d, MO); tmp %= MO; } tmp *= invFac[i]; tmp %= MO; tmp *= invFac[K + 1 - i]; tmp %= MO; tmp *= (((K + 1 - i) % 2 != 0) ? -1 : +1); tmp %= MO; ans += tmp; ans %= MO; } ans = (ans % MO + MO) % MO; writeln(ans); } } catch (EOFException e) { } }