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;
namespace fft {
struct num {
  double x, y;
  num() { x = y = 0; }
  num(double x_, double y_) : x(x_), y(y_) {}
};
inline num operator+(num a, num b) { return num(a.x + b.x, a.y + b.y); }
inline num operator-(num a, num b) { return num(a.x - b.x, a.y - b.y); }
inline num operator*(num a, num b) {
  return num(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);
}
inline num conj(num a) { return num(a.x, -a.y); }
int base = 1;
vector<num> roots = {{0, 0}, {1, 0}};
vector<int> rev = {0, 1};
const double PI = static_cast<double>(acosl(-1.0));
void ensure_base(int nbase) {
  if (nbase <= base) {
    return;
  }
  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) {
    double angle = 2 * PI / (1 << (base + 1));
    for (int i = 1 << (base - 1); i < (1 << base); i++) {
      roots[i << 1] = roots[i];
      double angle_i = angle * (2 * i + 1 - (1 << base));
      roots[(i << 1) + 1] = num(cos(angle_i), sin(angle_i));
    }
    base++;
  }
}
void fft(vector<num>& a, int n = -1) {
  if (n == -1) {
    n = (int)a.size();
  }
  assert((n & (n - 1)) == 0);
  int 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 k = 1; k < n; k <<= 1) {
    for (int i = 0; i < n; i += 2 * k) {
      for (int j = 0; j < k; j++) {
        num z = a[i + j + k] * roots[j + k];
        a[i + j + k] = a[i + j] - z;
        a[i + j] = a[i + j] + z;
      }
    }
  }
}
vector<num> fa, fb;
vector<int64_t> square(const vector<int>& a) {
  if (a.empty()) {
    return {};
  }
  int need = (int)a.size() + (int)a.size() - 1;
  int nbase = 1;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if ((sz >> 1) > (int)fa.size()) {
    fa.resize(sz >> 1);
  }
  for (int i = 0; i < (sz >> 1); i++) {
    int x = (2 * i < (int)a.size() ? a[2 * i] : 0);
    int y = (2 * i + 1 < (int)a.size() ? a[2 * i + 1] : 0);
    fa[i] = num(x, y);
  }
  fft(fa, sz >> 1);
  num r(1.0 / (sz >> 1), 0.0);
  for (int i = 0; i <= (sz >> 2); i++) {
    int j = ((sz >> 1) - i) & ((sz >> 1) - 1);
    num fe = (fa[i] + conj(fa[j])) * num(0.5, 0);
    num fo = (fa[i] - conj(fa[j])) * num(0, -0.5);
    num aux = fe * fe + fo * fo * roots[(sz >> 1) + i] * roots[(sz >> 1) + i];
    num tmp = fe * fo;
    fa[i] = r * (conj(aux) + num(0, 2) * conj(tmp));
    fa[j] = r * (aux + num(0, 2) * tmp);
  }
  fft(fa, sz >> 1);
  vector<int64_t> res(need);
  for (int i = 0; i < need; i++) {
    res[i] = llround(i % 2 == 0 ? fa[i >> 1].x : fa[i >> 1].y);
  }
  return res;
}
vector<int64_t> multiply(const vector<int>& a, const vector<int>& b) {
  if (a.empty() || b.empty()) {
    return {};
  }
  if (a.size() == b.size() && a == b) {
    return square(a);
  }
  int need = (int)a.size() + (int)b.size() - 1;
  int nbase = 1;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if (sz > (int)fa.size()) {
    fa.resize(sz);
  }
  for (int i = 0; i < sz; i++) {
    int x = (i < (int)a.size() ? a[i] : 0);
    int y = (i < (int)b.size() ? b[i] : 0);
    fa[i] = num(x, y);
  }
  fft(fa, sz);
  num r(0, -0.25 / (sz >> 1));
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    num z = (fa[j] * fa[j] - conj(fa[i] * fa[i])) * r;
    fa[j] = (fa[i] * fa[i] - conj(fa[j] * fa[j])) * r;
    fa[i] = z;
  }
  for (int i = 0; i < (sz >> 1); i++) {
    num A0 = (fa[i] + fa[i + (sz >> 1)]) * num(0.5, 0);
    num A1 = (fa[i] - fa[i + (sz >> 1)]) * num(0.5, 0) * roots[(sz >> 1) + i];
    fa[i] = A0 + A1 * num(0, 1);
  }
  fft(fa, sz >> 1);
  vector<int64_t> res(need);
  for (int i = 0; i < need; i++) {
    res[i] = llround(i % 2 == 0 ? fa[i >> 1].x : fa[i >> 1].y);
  }
  return res;
}
vector<int> multiply_mod(const vector<int>& a, const vector<int>& b, int m) {
  if (a.empty() || b.empty()) {
    return {};
  }
  int eq = (a.size() == b.size() && a == b);
  int need = (int)a.size() + (int)b.size() - 1;
  int nbase = 0;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  if (sz > (int)fa.size()) {
    fa.resize(sz);
  }
  for (int i = 0; i < (int)a.size(); i++) {
    int x = (a[i] % m + m) % m;
    fa[i] = num(x & ((1 << 15) - 1), x >> 15);
  }
  fill(fa.begin() + a.size(), fa.begin() + sz, num{0, 0});
  fft(fa, sz);
  if (sz > (int)fb.size()) {
    fb.resize(sz);
  }
  if (eq) {
    copy(fa.begin(), fa.begin() + sz, fb.begin());
  } else {
    for (int i = 0; i < (int)b.size(); i++) {
      int x = (b[i] % m + m) % m;
      fb[i] = num(x & ((1 << 15) - 1), x >> 15);
    }
    fill(fb.begin() + b.size(), fb.begin() + sz, num{0, 0});
    fft(fb, sz);
  }
  double ratio = 0.25 / sz;
  num r2(0, -1);
  num r3(ratio, 0);
  num r4(0, -ratio);
  num r5(0, 1);
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    num a1 = (fa[i] + conj(fa[j]));
    num a2 = (fa[i] - conj(fa[j])) * r2;
    num b1 = (fb[i] + conj(fb[j])) * r3;
    num b2 = (fb[i] - conj(fb[j])) * r4;
    if (i != j) {
      num c1 = (fa[j] + conj(fa[i]));
      num c2 = (fa[j] - conj(fa[i])) * r2;
      num d1 = (fb[j] + conj(fb[i])) * r3;
      num d2 = (fb[j] - conj(fb[i])) * r4;
      fa[i] = c1 * d1 + c2 * d2 * r5;
      fb[i] = c1 * d2 + c2 * d1;
    }
    fa[j] = a1 * b1 + a2 * b2 * r5;
    fb[j] = a1 * b2 + a2 * b1;
  }
  fft(fa, sz);
  fft(fb, sz);
  vector<int> res(need);
  for (int i = 0; i < need; i++) {
    int64_t aa = llround(fa[i].x);
    int64_t bb = llround(fb[i].x);
    int64_t cc = llround(fa[i].y);
    res[i] = static_cast<int>((aa + ((bb % m) << 15) + ((cc % m) << 30)) % m);
  }
  return res;
}
}  // namespace fft
const int N = (int)2e5 + 123, inf = 1e9, mod = 998244353;
const long long INF = 1e18;
vector<int> t[N << 2];
int n, k, q, a[N], b[N];
void build(int v, int tl, int tr) {
  if (tl == tr) {
    t[v].clear();
    t[v].push_back(1);
    t[v].push_back(b[tl]);
    return;
  }
  int tm = (tl + tr) >> 1;
  build(v << 1, tl, tm);
  build(v << 1 | 1, tm + 1, tr);
  t[v] = fft::multiply_mod(t[v << 1], t[v << 1 | 1], mod);
}
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  scanf("%d", &q);
  while (q--) {
    for (int i = 1; i <= n; i++) b[i] = a[i];
    int type;
    scanf("%d", &type);
    if (type == 1) {
      int q, i, d;
      scanf("%d%d%d", &q, &i, &d);
      b[i] = d;
      for (int i = 1; i <= n; i++) b[i] = ((q - b[i]) % mod + mod) % mod;
    } else {
      int q, l, r, d;
      scanf("%d%d%d%d", &q, &l, &r, &d);
      for (int i = l; i <= r; i++) b[i] += d;
      for (int i = 1; i <= n; i++) b[i] = ((q - b[i]) % mod + mod) % mod;
    }
    build(1, 1, n);
    printf("%d\n", t[1][k] % mod);
  }
  return 0;
}