Marmot found a row with n pillars. The i-th pillar has the height of hi meters. Starting from one pillar i1, Marmot wants to jump on the pillars i2, ..., ik. (1 ≤ i1 < i2 < ... < ik ≤ n). From a pillar i Marmot can jump on a pillar j only if i < j and |hi - hj| ≥ d, where |x| is the absolute value of the number x.

Now Marmot is asking you find out a jump sequence with maximal length and print it.

Input

The first line contains two integers n and d (1 ≤ n ≤ 105, 0 ≤ d ≤ 109).

The second line contains n numbers h1, h2, ..., hn (1 ≤ hi ≤ 1015).

Output

The first line should contain one integer k, the maximal length of a jump sequence.

The second line should contain k integers i1, i2, ..., ik (1 ≤ i1 < i2 < ... < ik ≤ n), representing the pillars' indices from the maximal length jump sequence.

If there is more than one maximal length jump sequence, print any.

Examples

Input

5 2
1 3 6 7 4


Output

4
1 2 3 5 


Input

10 3
2 1 3 6 9 11 7 3 20 18


Output

6
1 4 6 7 8 9 

Note

In the first example Marmot chooses the pillars 1, 2, 3, 5 with the heights 1, 3, 6, 4. Another jump sequence of length 4 is 1, 2, 4, 5.
#include <bits/stdc++.h>
namespace IO {
const int SIZE = (1 << 20) + 1;
char ibuf[SIZE], *iS, *iT, obuf[SIZE], *oS = obuf, *oT = obuf + SIZE - 1;
char _st[55];
int _qr = 0;
inline char gc() {
  return (iS == iT ? iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
          (iS == iT ? EOF : *iS++) : *iS++);
}
inline void qread() {}
template <class T1, class... T2>
inline void qread(T1 &IEE, T2 &...ls) {
  register T1 __ = 0, ___ = 1;
  register char ch;
  while (!isdigit(ch = gc())) ___ = (ch == '-') ? -___ : ___;
  do {
    __ = (__ << 1) + (__ << 3) + (ch ^ 48);
  } while (isdigit(ch = gc()));
  __ *= ___;
  IEE = __;
  qread(ls...);
  return;
}
template <class T>
inline void QreadArr(T Begin, T End) {
  while (Begin != End) {
    qread(*Begin);
    ++Begin;
  }
}
inline void flush() {
  fwrite(obuf, 1, oS - obuf, stdout);
  oS = obuf;
  return;
}
inline void putc_(char _x) {
  *oS++ = _x;
  if (oS == oT) flush();
}
inline void qwrite() {}
template <class T1, class... T2>
inline void qwrite(T1 IEE, T2... ls) {
  if (!IEE) putc_('0');
  if (IEE < 0) putc_('-'), IEE = -IEE;
  while (IEE) _st[++_qr] = IEE % 10 + '0', IEE /= 10;
  while (_qr) putc_(_st[_qr--]);
  qwrite(ls...);
  return;
}
template <class T>
inline void WriteArr(T Begin, T End) {
  const char Kg = ' ', Edl = '\n';
  while (Begin != End) {
    qwrite(*Begin);
    ++Begin;
    putc_(Kg);
  }
  putc_(Edl);
}
struct Flusher_ {
  ~Flusher_() { flush(); }
} io_flusher;
}  // namespace IO
using namespace IO;
using namespace std;
mt19937_64 rnd(chrono::steady_clock::now().time_since_epoch().count());
long long My_Rand(long long Mod) { return (unsigned long long)(rnd()) % Mod; }
template <class T1, class T2>
T1 Min(const T1 x, const T2 y) {
  return x > y ? y : x;
}
template <class T1, class T2>
T1 Max(const T1 x, const T2 y) {
  return x > y ? x : y;
}
template <class T1, class T2>
void To_max(T1 &x, const T2 y) {
  x < y ? x = y : x = x;
}
template <class T1, class T2>
void To_min(T1 &x, const T2 y) {
  x > y ? x = y : x = x;
}
inline long long qmul(long long x, long long y, long long p) {
  long long l = x * (y >> 25) % p * (1 << 25) % p;
  long long r = x * (y & ((1 << 25) - 1)) % p;
  return (l + r) % p;
}
inline long long qpow(long long n, long long base, long long mod = 1e18) {
  long long ret = 1;
  while (n) {
    if (n & 1) ret = ret * base % mod;
    base = base * base % mod;
    n >>= 1;
  }
  return ret % mod;
}
inline long long gcd(long long x, long long y) {
  return !y ? x : gcd(y, x % y);
}
inline long long lcm(long long x, long long y) { return x / gcd(x, y) * y; }
void InitHash(unsigned long long &base, int &prime, unsigned long long &mod) {
  base = 131, prime = 233317, mod = 212370440130137957ll;
}
const long long N = 1e5 + 5;
long long n, d, l;
long long a[N], t[N];
long long dp[N], nxt[N];
long long t1[N], t2[N];
inline long long lowbit(long long x) { return x & (-x); }
long long mx(long long x, long long y) { return dp[x] < dp[y] ? y : x; }
void u1(long long x, long long v) {
  while (x <= n) t1[x] = mx(t1[x], v), x += lowbit(x);
}
void u2(long long x, long long v) {
  while (x <= n) t2[x] = mx(t2[x], v), x += lowbit(x);
}
long long q1(long long x) {
  long long ret = 0;
  while (x) ret = mx(ret, t1[x]), x -= lowbit(x);
  return ret;
}
long long q2(long long x) {
  long long ret = 0;
  while (x) ret = mx(ret, t2[x]), x -= lowbit(x);
  return ret;
}
signed main() {
  qread(n, d);
  for (long long i = (1); i <= (n); ++i) qread(a[i]), t[i] = a[i];
  sort(t + 1, t + n + 1);
  l = unique(t + 1, t + n + 1) - t - 1;
  for (long long i = (n); i >= (1); --i) {
    long long p1 = lower_bound(t + 1, t + l + 1, a[i] + d) - t,
              p2 = upper_bound(t + 1, t + l + 1, a[i] - d) - t - 1;
    long long pos = mx(q1(p2), q2(l - p1 + 1));
    dp[i] = dp[pos] + 1;
    nxt[i] = pos;
    pos = lower_bound(t + 1, t + l + 1, a[i]) - t;
    u1(pos, i);
    u2(l - pos + 1, i);
  }
  long long ans = 0;
  for (long long i = (1); i <= (n); ++i) ans = mx(ans, i);
  printf("%lld\n", dp[ans]);
  while (ans) {
    printf("%lld ", ans);
    ans = nxt[ans];
  }
  return 0;
}
