Problem: While roaming the mystic areas of Stonefalls, in order to drop legendary loot, an adventurer was given a quest as follows. He was given an array A = {a_1,a_2,...,a_N } of length N, and a number K.

Define array B as B(q, A) =  { q-a_1, q-a_2, ..., q-a_N }. Define function F as F(B,K) being sum of products of all K-tuples of elements in array B. For example, if the array B is [2,3,4,5], and with K=3, sum of products of all 3-tuples is $$$F(B, 3) = 2*3*4+2*3*5+3*4*5+2*4*5$$$

He was then given a number Q, number of queries of two types: 

  * Type 1: Given q, i, and d calculate F(B(q, A), K) where we make change to initial array as A[i] = d. 
  * Type 2: Given q, L, R, and d calculate F(B(q, A), K) where we make change to initial array as A[i] = A[i] + d for all i in range [L, R] inclusive. 



All changes are temporarily made to initial array, and don't propagate to following queries. Help the adventurer calculate the answer to a quest, and finally get that loot!

Input

In the first two lines, numbers N (1 ≤ N ≤ 2*10^4) and K (1 ≤ K ≤ N), the length of initial array A, and tuple size, followed by a_1,a_2,a_3,…,a_N (0 ≤ a_i ≤ 10^9) , elements of array A, in the next line. Then follows number Q (Q ≤ 10), number of queries. In the next Q lines come queries of the form: 

  * 1 q i d, for type 1, 
  * 2 q L R d, for type 2, 



as explained above (0 ≤ q, d ≤ 10^9, 1 ≤ i,L,R ≤ N)

Output

Print Q lines, the answers to queries, modulo 998244353.

Example

Input


5
2
1 2 3 4 5
3
1 6 1 1
1 6 5 2
2 6 2 3 1


Output


85
127
63

Note

In the first query array A = [1, 2, 3, 4, 5], B = [5, 4, 3, 2, 1], sum of products of 2-tuples = 85.

In second query array A = [1, 2, 3, 4, 2], B = [5, 4, 3, 2, 4], sum of products of 2-tuples = 127

In third query array A = [1, 3, 4, 4, 5], B = [5, 3, 2, 2, 1], sum of products of 2-tuples = 63

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using db = double;
using pii = pair<int, int>;
using vi = vector<int>;
const int md = 998244353;
inline void add(int &x, int y) {
  x += y;
  if (x >= md) {
    x -= md;
  }
}
inline void sub(int &x, int y) {
  x -= y;
  if (x < 0) {
    x += md;
  }
}
inline int mul(int x, int y) { return (long long)x * y % md; }
inline int power(int x, int y) {
  int res = 1;
  for (; y; y >>= 1, x = mul(x, x)) {
    if (y & 1) {
      res = mul(res, x);
    }
  }
  return res;
}
inline int inv(int a) {
  a %= md;
  if (a < 0) {
    a += md;
  }
  int b = md, u = 0, v = 1;
  while (a) {
    int t = b / a;
    b -= t * a;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  if (u < 0) {
    u += md;
  }
  return u;
}
namespace ntt {
int base = 1, root = -1, max_base = -1;
vector<int> rev = {0, 1}, roots = {0, 1};
void init() {
  int temp = md - 1;
  max_base = 0;
  while (temp % 2 == 0) {
    temp >>= 1;
    ++max_base;
  }
  root = 2;
  while (true) {
    if (power(root, 1 << max_base) == 1 &&
        power(root, 1 << max_base - 1) != 1) {
      break;
    }
    ++root;
  }
}
void ensure_base(int nbase) {
  if (max_base == -1) {
    init();
  }
  if (nbase <= base) {
    return;
  }
  assert(nbase <= max_base);
  rev.resize(1 << nbase);
  for (int i = 0; i < 1 << nbase; ++i) {
    rev[i] = rev[i >> 1] >> 1 | (i & 1) << nbase - 1;
  }
  roots.resize(1 << nbase);
  while (base < nbase) {
    int z = power(root, 1 << max_base - 1 - base);
    for (int i = 1 << base - 1; i < 1 << base; ++i) {
      roots[i << 1] = roots[i];
      roots[i << 1 | 1] = mul(roots[i], z);
    }
    ++base;
  }
}
void dft(vector<int> &a) {
  int n = a.size(), zeros = __builtin_ctz(n);
  ensure_base(zeros);
  int shift = base - zeros;
  for (int i = 0; i < n; ++i) {
    if (i < rev[i] >> shift) {
      swap(a[i], a[rev[i] >> shift]);
    }
  }
  for (int i = 1; i < n; i <<= 1) {
    for (int j = 0; j < n; j += i << 1) {
      for (int k = 0; k < i; ++k) {
        int x = a[j + k], y = mul(a[j + k + i], roots[i + k]);
        a[j + k] = (x + y) % md;
        a[j + k + i] = (x + md - y) % md;
      }
    }
  }
}
vector<int> multiply(vector<int> a, vector<int> b) {
  int need = a.size() + b.size() - 1, nbase = 0;
  while (1 << nbase < need) {
    ++nbase;
  }
  ensure_base(nbase);
  int sz = 1 << nbase;
  a.resize(sz);
  b.resize(sz);
  bool equal = a == b;
  dft(a);
  if (equal) {
    b = a;
  } else {
    dft(b);
  }
  int inv_sz = inv(sz);
  for (int i = 0; i < sz; ++i) {
    a[i] = mul(mul(a[i], b[i]), inv_sz);
  }
  reverse(a.begin() + 1, a.end());
  dft(a);
  a.resize(need);
  return a;
}
vector<int> inverse(vector<int> a) {
  int n = a.size(), m = n + 1 >> 1;
  if (n == 1) {
    return vector<int>(1, inv(a[0]));
  } else {
    vector<int> b = inverse(vector<int>(a.begin(), a.begin() + m));
    int need = n << 1, nbase = 0;
    while (1 << nbase < need) {
      ++nbase;
    }
    ensure_base(nbase);
    int sz = 1 << nbase;
    a.resize(sz);
    b.resize(sz);
    dft(a);
    dft(b);
    int inv_sz = inv(sz);
    for (int i = 0; i < sz; ++i) {
      a[i] = mul(mul(md + 2 - mul(a[i], b[i]), b[i]), inv_sz);
    }
    reverse(a.begin() + 1, a.end());
    dft(a);
    a.resize(n);
    return a;
  }
}
}  // namespace ntt
using ntt::inverse;
using ntt::multiply;
vector<int> &operator+=(vector<int> &a, const vector<int> &b) {
  if (a.size() < b.size()) {
    a.resize(b.size());
  }
  for (int i = 0; i < b.size(); ++i) {
    add(a[i], b[i]);
  }
  return a;
}
vector<int> operator+(const vector<int> &a, const vector<int> &b) {
  vector<int> c = a;
  return c += b;
}
vector<int> &operator-=(vector<int> &a, const vector<int> &b) {
  if (a.size() < b.size()) {
    a.resize(b.size());
  }
  for (int i = 0; i < b.size(); ++i) {
    sub(a[i], b[i]);
  }
  return a;
}
vector<int> operator-(const vector<int> &a, const vector<int> &b) {
  vector<int> c = a;
  return c -= b;
}
vector<int> &operator*=(vector<int> &a, const vector<int> &b) {
  if (min(a.size(), b.size()) < 128) {
    vector<int> c = a;
    a.assign(a.size() + b.size() - 1, 0);
    for (int i = 0; i < c.size(); ++i) {
      for (int j = 0; j < b.size(); ++j) {
        add(a[i + j], mul(c[i], b[j]));
      }
    }
  } else {
    a = multiply(a, b);
  }
  return a;
}
vector<int> operator*(const vector<int> &a, const vector<int> &b) {
  vector<int> c = a;
  return c *= b;
}
vector<int> &operator/=(vector<int> &a, const vector<int> &b) {
  int n = a.size(), m = b.size();
  if (n < m) {
    a.clear();
  } else {
    vector<int> c = b;
    reverse(a.begin(), a.end());
    reverse(c.begin(), c.end());
    c.resize(n - m + 1);
    a *= inverse(c);
    a.erase(a.begin() + n - m + 1, a.end());
    reverse(a.begin(), a.end());
  }
  return a;
}
vector<int> operator/(const vector<int> &a, const vector<int> &b) {
  vector<int> c = a;
  return c /= b;
}
vector<int> &operator%=(vector<int> &a, const vector<int> &b) {
  int n = a.size(), m = b.size();
  if (n >= m) {
    vector<int> c = (a / b) * b;
    a.resize(m - 1);
    for (int i = 0; i < m - 1; ++i) {
      sub(a[i], c[i]);
    }
  }
  return a;
}
vector<int> operator%(const vector<int> &a, const vector<int> &b) {
  vector<int> c = a;
  return c %= b;
}
vector<int> derivative(const vector<int> &a) {
  int n = a.size();
  vector<int> b(n - 1);
  for (int i = 1; i < n; ++i) {
    b[i - 1] = mul(a[i], i);
  }
  return b;
}
vector<int> primitive(const vector<int> &a) {
  int n = a.size();
  vector<int> b(n + 1), invs(n + 1);
  for (int i = 1; i <= n; ++i) {
    invs[i] = i == 1 ? 1 : mul(md - md / i, invs[md % i]);
    b[i] = mul(a[i - 1], invs[i]);
  }
  return b;
}
vector<int> logarithm(const vector<int> &a) {
  vector<int> b = primitive(derivative(a) * inverse(a));
  b.resize(a.size());
  return b;
}
vector<int> exponent(const vector<int> &a) {
  vector<int> b(1, 1);
  while (b.size() < a.size()) {
    vector<int> c(a.begin(), a.begin() + min(a.size(), b.size() << 1));
    add(c[0], 1);
    vector<int> old_b = b;
    b.resize(b.size() << 1);
    c -= logarithm(b);
    c *= old_b;
    for (int i = b.size() >> 1; i < b.size(); ++i) {
      b[i] = c[i];
    }
  }
  b.resize(a.size());
  return b;
}
vector<int> power(const vector<int> &a, int m) {
  int n = a.size(), p = -1;
  vector<int> b(n);
  for (int i = 0; i < n; ++i) {
    if (a[i]) {
      p = i;
      break;
    }
  }
  if (p == -1) {
    b[0] = !m;
    return b;
  }
  if ((long long)m * p >= n) {
    return b;
  }
  int mu = power(a[p], m), di = inv(a[p]);
  vector<int> c(n - m * p);
  for (int i = 0; i < n - m * p; ++i) {
    c[i] = mul(a[i + p], di);
  }
  c = logarithm(c);
  for (int i = 0; i < n - m * p; ++i) {
    c[i] = mul(c[i], m);
  }
  c = exponent(c);
  for (int i = 0; i < n - m * p; ++i) {
    b[i + m * p] = mul(c[i], mu);
  }
  return b;
}
vector<int> sqrt(const vector<int> &a) {
  vector<int> b(1, 1);
  while (b.size() < a.size()) {
    vector<int> c(a.begin(), a.begin() + min(a.size(), b.size() << 1));
    vector<int> old_b = b;
    b.resize(b.size() << 1);
    c *= inverse(b);
    for (int i = b.size() >> 1; i < b.size(); ++i) {
      b[i] = mul(c[i], md + 1 >> 1);
    }
  }
  b.resize(a.size());
  return b;
}
vector<int> multiply_all(int l, int r, vector<vector<int>> &all) {
  if (l > r) {
    return vector<int>();
  } else if (l == r) {
    return all[l];
  } else {
    int y = l + r >> 1;
    return multiply_all(l, y, all) * multiply_all(y + 1, r, all);
  }
}
vector<int> evaluate(const vector<int> &f, const vector<int> &x) {
  int n = x.size();
  if (!n) {
    return vector<int>();
  }
  vector<vector<int>> up(n * 2);
  for (int i = 0; i < n; ++i) {
    up[i + n] = vector<int>{(md - x[i]) % md, 1};
  }
  for (int i = n - 1; i; --i) {
    up[i] = up[i << 1] * up[i << 1 | 1];
  }
  vector<vector<int>> down(n * 2);
  down[1] = f % up[1];
  for (int i = 2; i < n * 2; ++i) {
    down[i] = down[i >> 1] % up[i];
  }
  vector<int> y(n);
  for (int i = 0; i < n; ++i) {
    y[i] = down[i + n][0];
  }
  return y;
}
vector<int> interpolate(const vector<int> &x, const vector<int> &y) {
  int n = x.size();
  vector<vector<int>> up(n * 2);
  for (int i = 0; i < n; ++i) {
    up[i + n] = vector<int>{(md - x[i]) % md, 1};
  }
  for (int i = n - 1; i; --i) {
    up[i] = up[i << 1] * up[i << 1 | 1];
  }
  vector<int> a = evaluate(derivative(up[1]), x);
  for (int i = 0; i < n; ++i) {
    a[i] = mul(y[i], inv(a[i]));
  }
  vector<vector<int>> down(n * 2);
  for (int i = 0; i < n; ++i) {
    down[i + n] = vector<int>(1, a[i]);
  }
  for (int i = n - 1; i; --i) {
    down[i] = down[i << 1] * up[i << 1 | 1] + down[i << 1 | 1] * up[i << 1];
  }
  return down[1];
}
const int P = 998244353;
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, k, q;
  cin >> n >> k;
  vi a(n + 1), b(n + 1);
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (cin >> q; q; q--) {
    int op;
    cin >> op;
    if (op == 1) {
      int v, x, d;
      cin >> v >> x >> d;
      for (int i = 1; i <= n; i++) b[i] = v - a[i];
      b[x] = v - d;
      vector<vi> all;
      for (int i = 1; i <= n; i++) all.push_back({1, (b[i] % P + P) % P});
      cout << multiply_all(0, all.size() - 1, all)[k] << '\n';
    } else {
      int v, l, r, d;
      cin >> v >> l >> r >> d;
      for (int i = 1; i <= n; i++) b[i] = v - a[i];
      for (int i = l; i <= r; i++) b[i] -= d;
      vector<vi> all;
      for (int i = 1; i <= n; i++) all.push_back({1, (b[i] % P + P) % P});
      cout << multiply_all(0, all.size() - 1, all)[k] << '\n';
    }
  }
  fprintf(stderr, "time=%.4f\n", (db)clock() / CLOCKS_PER_SEC);
  return 0;
}