#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int pct(long long x) { return __builtin_popcountll(x); }
constexpr int bits(int x) { return x == 0 ? 0 : 31 - __builtin_clz(x); }
constexpr int bits(long long x) { return x == 0 ? 0 : 63 - __builtin_clzll(x); }
constexpr int p2(int x) { return 1 << x; }
constexpr int msk2(int x) { return p2(x) - 1; }
template <class T, class U>
T ipow(T a, U p) {
  T ans = 1;
  assert(p >= 0);
  for (; p; p /= 2, a *= a)
    if (p & 1) ans *= a;
  return ans;
}
template <class T, class U>
T ipow(T a, U p, T m) {
  T ans = 1;
  assert(p >= 0);
  for (; p; p /= 2, a = (a * a) % m)
    if (p & 1) ans = (ans * a) % m;
  return ans;
}
template <class T, class U>
T fstTrue(T lo, T hi, U f) {
  hi++;
  assert(lo <= hi);
  while (lo < hi) {
    T mid = lo + (hi - lo) / 2;
    f(mid) ? hi = mid : lo = mid + 1;
  }
  return lo;
}
template <class T, class U>
T lstTrue(T lo, T hi, U f) {
  lo--;
  assert(lo <= hi);
  while (lo < hi) {
    T mid = lo + (hi - lo + 1) / 2;
    f(mid) ? lo = mid : hi = mid - 1;
  }
  return lo;
}
template <class T>
T sum(vector<T> &v) {
  if (v.empty()) return 0LL;
  T sum = v[0];
  for (int i = 1; i < (int)v.size(); i++) {
    sum += v[i];
  }
  return sum;
}
template <class F>
F posmod(F a, F b) {
  return ((a % b) + b) % b;
}
template <class F>
struct Point {
  F x, y;
  Point() : x(0), y(0) {}
  Point(const F &cx, const F &cy) : x(cx), y(cy) {}
};
template <class F>
F ceildiv(F a, F d) {
  F res = a / d;
  if (res * d != a) res += 1 & ((a < 0) ^ (d > 0));
  return res;
}
template <class F>
F sq(F a) {
  return a * a;
}
long long inv(long long a, long long b) {
  return 1 < a ? b - inv(b % a, a) * b / a : 1;
}
template <class T>
bool ckmin(T &a, const T &b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool ckmax(T &a, const T &b) {
  return a < b ? a = b, 1 : 0;
}
int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
int rint(int a, int b) { return uniform_int_distribution<int>(a, b)(rng); }
double rdouble(double a, double b) {
  return uniform_real_distribution<double>(a, b)(rng);
}
template <class T>
void remdup(vector<T> &v) {
  sort((v).begin(), (v).end());
  v.erase(unique((v).begin(), (v).end()), end(v));
}
template <class F>
void print(const Point<F> &point) {
  cout << "x: " << point.x << "\ty: " << point.y << '\n';
}
template <class F>
void print(const F a[], int n) {
  for (int i = 0; i < n; i++) {
    if (i > 0) cout << ' ';
    cout << a[i];
  }
  cout << '\n';
}
template <class F>
void print(const vector<F> &a) {
  for (int i = 0; i < (int)a.size(); i++) {
    if (i > 0) cout << ' ';
    cout << a[i];
  }
  cout << '\n';
}
template <class F>
void print2(const vector<vector<F>> &a) {
  for (int i = 0; i < (int)a.size(); i++) {
    for (int j = 0; j < (int)a[i].size(); j++) {
      if (j > 0) cout << ' ';
      cout << a[i][j];
    }
    cout << '\n';
  }
}
template <class F>
void fill2(vector<vector<F>> &a, F val) {
  for (int i = 0; i < (int)a.size(); i++) {
    for (int j = 0; j < (int)a[i].size(); j++) {
      a[i][j] = val;
    }
  }
}
template <class F>
void fill3(vector<vector<vector<F>>> &a, F val) {
  for (int i = 0; i < (int)a.size(); i++) {
    for (int j = 0; j < (int)a[i].size(); j++) {
      for (int k = 0; k < (int)a[i][j].size(); k++) {
        a[i][j][k] = val;
      }
    }
  }
}
int gen_base(const int before, const int after) {
  int base = rint(before + 1, after);
  return base % 2 == 0 ? base - 1 : base;
}
struct phash {
  static const int mod = (int)1e9 + 123;
  static vector<int> pow1;
  static vector<ull> pow2;
  static int base;
  vector<int> pref1;
  vector<ull> pref2;
  phash(const string &s)
      : pref1(int((s).size()) + 1u, 0), pref2(int((s).size()) + 1u, 0) {
    assert(base < mod);
    const int n = int((s).size());
    while (int((pow1).size()) <= n) {
      pow1.push_back((int)((ll)pow1.back() * base % mod));
      pow2.push_back(pow2.back() * base);
    }
    for (int i = 0; i < n; i++) {
      assert(base > s[i]);
      pref1[i + 1] = (int)((pref1[i] + (ll)s[i] * pow1[i]) % mod);
      pref2[i + 1] = pref2[i] + s[i] * pow2[i];
    }
  }
  inline std::pair<int, ull> operator()(const int pos, const int len,
                                        int mxPow = -1) const {
    if (mxPow == -1) mxPow = (int)pref1.size() - 1;
    int hash1 = pref1[pos + len] - pref1[pos];
    ull hash2 = pref2[pos + len] - pref2[pos];
    if (hash1 < 0) hash1 += mod;
    if (mxPow != 0) {
      hash1 = (int)((ll)hash1 * pow1[mxPow - (pos + len - 1)] % mod);
      hash2 *= pow2[mxPow - (pos + len - 1)];
    }
    return {hash1, hash2};
  }
};
vector<int> phash::pow1{1};
vector<ull> phash::pow2{1};
int phash::base = gen_base(256, phash::mod);
struct mi {
  ll v;
  explicit operator ll() const { return v; }
  mi() { v = 0; }
  mi(ll _v) {
    v = (-(int)(1e9 + 7) < _v && _v < (int)(1e9 + 7)) ? _v
                                                      : _v % (int)(1e9 + 7);
    if (v < 0) v += (int)(1e9 + 7);
  }
  friend bool operator==(const mi &a, const mi &b) { return a.v == b.v; }
  friend bool operator!=(const mi &a, const mi &b) { return !(a == b); }
  friend bool operator<(const mi &a, const mi &b) { return a.v < b.v; }
  mi &operator+=(const mi &m) {
    if ((v += m.v) >= (int)(1e9 + 7)) v -= (int)(1e9 + 7);
    return *this;
  }
  mi &operator-=(const mi &m) {
    if ((v -= m.v) < 0) v += (int)(1e9 + 7);
    return *this;
  }
  mi &operator*=(const mi &m) {
    v = v * m.v % (int)(1e9 + 7);
    return *this;
  }
  mi &operator/=(const mi &m) { return (*this) *= inv(m); }
  friend mi pow(mi a, ll p) {
    mi ans = 1;
    assert(p >= 0);
    for (; p; p /= 2, a *= a)
      if (p & 1) ans *= a;
    return ans;
  }
  friend mi inv(const mi &a) {
    assert(a.v != 0);
    return pow(a, (int)(1e9 + 7) - 2);
  }
  mi operator-() const { return mi(-v); }
  mi &operator++() { return *this += 1; }
  mi &operator--() { return *this -= 1; }
  mi operator++(int) {
    mi temp;
    temp.v = v++;
    return temp;
  }
  mi operator--(int) {
    mi temp;
    temp.v = v--;
    return temp;
  }
  friend mi operator+(mi a, const mi &b) { return a += b; }
  friend mi operator-(mi a, const mi &b) { return a -= b; }
  friend mi operator*(mi a, const mi &b) { return a *= b; }
  friend mi operator/(mi a, const mi &b) { return a /= b; }
  friend ostream &operator<<(ostream &os, const mi &m) {
    os << m.v;
    return os;
  }
  friend istream &operator>>(istream &is, mi &m) {
    ll x;
    is >> x;
    m.v = x;
    return is;
  }
};
const int MX = 1e6;
bool facinit = false;
mi facs[MX];
mi facInvs[MX];
mi ncr(mi _a, mi _b) {
  ll a = (ll)_a;
  ll b = (ll)_b;
  assert(facinit && a < MX && b < MX);
  assert(a >= 0 && b >= 0 && b <= a);
  if (b > a || a < 0 || b < 0) return 0;
  mi cur = facs[a];
  cur = cur * facInvs[b];
  cur = cur * facInvs[a - b];
  return cur;
}
void initFacs() {
  facs[0] = 1;
  for (int i = (1); i < (MX); ++i) facs[i] = i * facs[i - 1];
  facInvs[MX - 1] = inv(facs[MX - 1]);
  for (int i = (MX - 1) - 1; i >= 0; i--) facInvs[i] = facInvs[i + 1] * (i + 1);
  facinit = true;
}
void solve() {
  int n;
  cin >> n;
  int d;
  cin >> d;
  vector<int> a = vector<int>((n));
  for (int i = 0; i < (n); ++i) cin >> a[i];
  ;
  vector<bool> visited(n, false);
  int longest = 0;
  for (int i = 0; i < (n); ++i) {
    if (!visited[i]) {
      int j = i;
      int iteration = 0;
      while (a[j] != 0) {
        if (++iteration > 2 * n) {
          cout << -1 << '\n';
          return;
        }
        visited[j] = true;
        j = (n + j - d) % n;
        assert(j >= 0 && j < n);
        if (j == i) {
          {
            cout << "-1\n";
            return;
          };
        }
      }
      int zerostart = j;
      int c = 0;
      int iteration2 = 0;
      j = (n + j - d) % n;
      assert(j >= 0 && j < n);
      while (j != zerostart) {
        visited[j] = true;
        if (++iteration2 > 2 * n) {
          cout << -2 << '\n';
          return;
        }
        if (a[j] == 1) c++;
        j = (n + j - d) % n;
        assert(j >= 0 && j < n);
        if (a[j] == 0) {
          ckmax(longest, c);
          c = 0;
        }
      }
    }
  }
  cout << longest << '\n';
}
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

You are given an array a[0 … n - 1] = [a_0, a_1, …, a_{n - 1}] of zeroes and ones only. Note that in this problem, unlike the others, the array indexes are numbered from zero, not from one.

In one step, the array a is replaced by another array of length n according to the following rules: 

  1. First, a new array a^{→ d} is defined as a cyclic shift of the array a to the right by d cells. The elements of this array can be defined as a^{→ d}_i = a_{(i + n - d) mod n}, where (i + n - d) mod n is the remainder of integer division of i + n - d by n. 

It means that the whole array a^{→ d} can be represented as a sequence $$$a^{→ d} = [a_{n - d}, a_{n - d + 1}, …, a_{n - 1}, a_0, a_1, …, a_{n - d - 1}]$$$

  2. Then each element of the array a_i is replaced by a_i  \&  a^{→ d}_i, where \& is a logical "AND" operator. 



For example, if a = [0, 0, 1, 1] and d = 1, then a^{→ d} = [1, 0, 0, 1] and the value of a after the first step will be [0  \&  1, 0  \&  0, 1  \&  0, 1  \&  1], that is [0, 0, 0, 1].

The process ends when the array stops changing. For a given array a, determine whether it will consist of only zeros at the end of the process. If yes, also find the number of steps the process will take before it finishes.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases.

The next 2t lines contain descriptions of the test cases. 

The first line of each test case description contains two integers: n (1 ≤ n ≤ 10^6) — array size and d (1 ≤ d ≤ n) — cyclic shift offset. The second line of the description contains n space-separated integers a_i (0 ≤ a_i ≤ 1) — elements of the array.

It is guaranteed that the sum of n over all test cases does not exceed 10^6.

Output

Print t lines, each line containing the answer to the corresponding test case. The answer to a test case should be a single integer — the number of steps after which the array will contain only zeros for the first time. If there are still elements equal to 1 in the array after the end of the process, print -1.

Example

Input


5
2 1
0 1
3 2
0 1 0
5 2
1 1 0 1 0
4 2
0 1 0 1
1 1
0


Output


1
1
3
-1
0

Note

In the third sample test case the array will change as follows: 

  1. At the beginning a = [1, 1, 0, 1, 0], and a^{→ 2} = [1, 0, 1, 1, 0]. Their element-by-element "AND" is equal to $$$[1  \&  1, 1  \&  0, 0  \&  1, 1  \&  1, 0  \&  0] = [1, 0, 0, 1, 0]$$$ 
  2. Now a = [1, 0, 0, 1, 0], then a^{→ 2} = [1, 0, 1, 0, 0]. Their element-by-element "AND" equals to $$$[1  \&  1, 0  \&  0, 0  \&  1, 1  \&  0, 0  \&  0] = [1, 0, 0, 0, 0]$$$ 
  3. And finally, when a = [1, 0, 0, 0, 0] we get a^{→ 2} = [0, 0, 1, 0, 0]. Their element-by-element "AND" equals to $$$[1  \&  0, 0  \&  0, 0  \&  1, 0  \&  0, 0  \&  0] = [0, 0, 0, 0, 0]$$$ 

Thus, the answer is 3 steps.

In the fourth sample test case, the array will not change as it shifts by 2 to the right, so each element will be calculated as 0  \&  0 or 1  \&  1 thus not changing its value. So the answer is -1, the array will never contain only zeros.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int pct(long long x) { return __builtin_popcountll(x); }
constexpr int bits(int x) { return x == 0 ? 0 : 31 - __builtin_clz(x); }
constexpr int bits(long long x) { return x == 0 ? 0 : 63 - __builtin_clzll(x); }
constexpr int p2(int x) { return 1 << x; }
constexpr int msk2(int x) { return p2(x) - 1; }
template <class T, class U>
T ipow(T a, U p) {
  T ans = 1;
  assert(p >= 0);
  for (; p; p /= 2, a *= a)
    if (p & 1) ans *= a;
  return ans;
}
template <class T, class U>
T ipow(T a, U p, T m) {
  T ans = 1;
  assert(p >= 0);
  for (; p; p /= 2, a = (a * a) % m)
    if (p & 1) ans = (ans * a) % m;
  return ans;
}
template <class T, class U>
T fstTrue(T lo, T hi, U f) {
  hi++;
  assert(lo <= hi);
  while (lo < hi) {
    T mid = lo + (hi - lo) / 2;
    f(mid) ? hi = mid : lo = mid + 1;
  }
  return lo;
}
template <class T, class U>
T lstTrue(T lo, T hi, U f) {
  lo--;
  assert(lo <= hi);
  while (lo < hi) {
    T mid = lo + (hi - lo + 1) / 2;
    f(mid) ? lo = mid : hi = mid - 1;
  }
  return lo;
}
template <class T>
T sum(vector<T> &v) {
  if (v.empty()) return 0LL;
  T sum = v[0];
  for (int i = 1; i < (int)v.size(); i++) {
    sum += v[i];
  }
  return sum;
}
template <class F>
F posmod(F a, F b) {
  return ((a % b) + b) % b;
}
template <class F>
struct Point {
  F x, y;
  Point() : x(0), y(0) {}
  Point(const F &cx, const F &cy) : x(cx), y(cy) {}
};
template <class F>
F ceildiv(F a, F d) {
  F res = a / d;
  if (res * d != a) res += 1 & ((a < 0) ^ (d > 0));
  return res;
}
template <class F>
F sq(F a) {
  return a * a;
}
long long inv(long long a, long long b) {
  return 1 < a ? b - inv(b % a, a) * b / a : 1;
}
template <class T>
bool ckmin(T &a, const T &b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool ckmax(T &a, const T &b) {
  return a < b ? a = b, 1 : 0;
}
int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
int rint(int a, int b) { return uniform_int_distribution<int>(a, b)(rng); }
double rdouble(double a, double b) {
  return uniform_real_distribution<double>(a, b)(rng);
}
template <class T>
void remdup(vector<T> &v) {
  sort((v).begin(), (v).end());
  v.erase(unique((v).begin(), (v).end()), end(v));
}
template <class F>
void print(const Point<F> &point) {
  cout << "x: " << point.x << "\ty: " << point.y << '\n';
}
template <class F>
void print(const F a[], int n) {
  for (int i = 0; i < n; i++) {
    if (i > 0) cout << ' ';
    cout << a[i];
  }
  cout << '\n';
}
template <class F>
void print(const vector<F> &a) {
  for (int i = 0; i < (int)a.size(); i++) {
    if (i > 0) cout << ' ';
    cout << a[i];
  }
  cout << '\n';
}
template <class F>
void print2(const vector<vector<F>> &a) {
  for (int i = 0; i < (int)a.size(); i++) {
    for (int j = 0; j < (int)a[i].size(); j++) {
      if (j > 0) cout << ' ';
      cout << a[i][j];
    }
    cout << '\n';
  }
}
template <class F>
void fill2(vector<vector<F>> &a, F val) {
  for (int i = 0; i < (int)a.size(); i++) {
    for (int j = 0; j < (int)a[i].size(); j++) {
      a[i][j] = val;
    }
  }
}
template <class F>
void fill3(vector<vector<vector<F>>> &a, F val) {
  for (int i = 0; i < (int)a.size(); i++) {
    for (int j = 0; j < (int)a[i].size(); j++) {
      for (int k = 0; k < (int)a[i][j].size(); k++) {
        a[i][j][k] = val;
      }
    }
  }
}
int gen_base(const int before, const int after) {
  int base = rint(before + 1, after);
  return base % 2 == 0 ? base - 1 : base;
}
struct phash {
  static const int mod = (int)1e9 + 123;
  static vector<int> pow1;
  static vector<ull> pow2;
  static int base;
  vector<int> pref1;
  vector<ull> pref2;
  phash(const string &s)
      : pref1(int((s).size()) + 1u, 0), pref2(int((s).size()) + 1u, 0) {
    assert(base < mod);
    const int n = int((s).size());
    while (int((pow1).size()) <= n) {
      pow1.push_back((int)((ll)pow1.back() * base % mod));
      pow2.push_back(pow2.back() * base);
    }
    for (int i = 0; i < n; i++) {
      assert(base > s[i]);
      pref1[i + 1] = (int)((pref1[i] + (ll)s[i] * pow1[i]) % mod);
      pref2[i + 1] = pref2[i] + s[i] * pow2[i];
    }
  }
  inline std::pair<int, ull> operator()(const int pos, const int len,
                                        int mxPow = -1) const {
    if (mxPow == -1) mxPow = (int)pref1.size() - 1;
    int hash1 = pref1[pos + len] - pref1[pos];
    ull hash2 = pref2[pos + len] - pref2[pos];
    if (hash1 < 0) hash1 += mod;
    if (mxPow != 0) {
      hash1 = (int)((ll)hash1 * pow1[mxPow - (pos + len - 1)] % mod);
      hash2 *= pow2[mxPow - (pos + len - 1)];
    }
    return {hash1, hash2};
  }
};
vector<int> phash::pow1{1};
vector<ull> phash::pow2{1};
int phash::base = gen_base(256, phash::mod);
struct mi {
  ll v;
  explicit operator ll() const { return v; }
  mi() { v = 0; }
  mi(ll _v) {
    v = (-(int)(1e9 + 7) < _v && _v < (int)(1e9 + 7)) ? _v
                                                      : _v % (int)(1e9 + 7);
    if (v < 0) v += (int)(1e9 + 7);
  }
  friend bool operator==(const mi &a, const mi &b) { return a.v == b.v; }
  friend bool operator!=(const mi &a, const mi &b) { return !(a == b); }
  friend bool operator<(const mi &a, const mi &b) { return a.v < b.v; }
  mi &operator+=(const mi &m) {
    if ((v += m.v) >= (int)(1e9 + 7)) v -= (int)(1e9 + 7);
    return *this;
  }
  mi &operator-=(const mi &m) {
    if ((v -= m.v) < 0) v += (int)(1e9 + 7);
    return *this;
  }
  mi &operator*=(const mi &m) {
    v = v * m.v % (int)(1e9 + 7);
    return *this;
  }
  mi &operator/=(const mi &m) { return (*this) *= inv(m); }
  friend mi pow(mi a, ll p) {
    mi ans = 1;
    assert(p >= 0);
    for (; p; p /= 2, a *= a)
      if (p & 1) ans *= a;
    return ans;
  }
  friend mi inv(const mi &a) {
    assert(a.v != 0);
    return pow(a, (int)(1e9 + 7) - 2);
  }
  mi operator-() const { return mi(-v); }
  mi &operator++() { return *this += 1; }
  mi &operator--() { return *this -= 1; }
  mi operator++(int) {
    mi temp;
    temp.v = v++;
    return temp;
  }
  mi operator--(int) {
    mi temp;
    temp.v = v--;
    return temp;
  }
  friend mi operator+(mi a, const mi &b) { return a += b; }
  friend mi operator-(mi a, const mi &b) { return a -= b; }
  friend mi operator*(mi a, const mi &b) { return a *= b; }
  friend mi operator/(mi a, const mi &b) { return a /= b; }
  friend ostream &operator<<(ostream &os, const mi &m) {
    os << m.v;
    return os;
  }
  friend istream &operator>>(istream &is, mi &m) {
    ll x;
    is >> x;
    m.v = x;
    return is;
  }
};
const int MX = 1e6;
bool facinit = false;
mi facs[MX];
mi facInvs[MX];
mi ncr(mi _a, mi _b) {
  ll a = (ll)_a;
  ll b = (ll)_b;
  assert(facinit && a < MX && b < MX);
  assert(a >= 0 && b >= 0 && b <= a);
  if (b > a || a < 0 || b < 0) return 0;
  mi cur = facs[a];
  cur = cur * facInvs[b];
  cur = cur * facInvs[a - b];
  return cur;
}
void initFacs() {
  facs[0] = 1;
  for (int i = (1); i < (MX); ++i) facs[i] = i * facs[i - 1];
  facInvs[MX - 1] = inv(facs[MX - 1]);
  for (int i = (MX - 1) - 1; i >= 0; i--) facInvs[i] = facInvs[i + 1] * (i + 1);
  facinit = true;
}
void solve() {
  int n;
  cin >> n;
  int d;
  cin >> d;
  vector<int> a = vector<int>((n));
  for (int i = 0; i < (n); ++i) cin >> a[i];
  ;
  vector<bool> visited(n, false);
  int longest = 0;
  for (int i = 0; i < (n); ++i) {
    if (!visited[i]) {
      int j = i;
      int iteration = 0;
      while (a[j] != 0) {
        if (++iteration > 2 * n) {
          cout << -1 << '\n';
          return;
        }
        visited[j] = true;
        j = (n + j - d) % n;
        assert(j >= 0 && j < n);
        if (j == i) {
          {
            cout << "-1\n";
            return;
          };
        }
      }
      int zerostart = j;
      int c = 0;
      int iteration2 = 0;
      j = (n + j - d) % n;
      assert(j >= 0 && j < n);
      while (j != zerostart) {
        visited[j] = true;
        if (++iteration2 > 2 * n) {
          cout << -2 << '\n';
          return;
        }
        if (a[j] == 1) c++;
        j = (n + j - d) % n;
        assert(j >= 0 && j < n);
        if (a[j] == 0) {
          ckmax(longest, c);
          c = 0;
        }
      }
    }
  }
  cout << longest << '\n';
}
int32_t main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int t = 1;
  cin >> t;
  while (t--) {
    solve();
  }
  return 0;
}

```