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;
const double eps = 1e-8;
const double pi = acos(-1.0);
template <class T>
long long chkmin(T &a, T b) {
  return a > b ? a = b, 1 : 0;
}
template <class T>
long long chkmax(T &a, T b) {
  return a < b ? a = b, 1 : 0;
}
template <class T>
T sqr(T a) {
  return a * a;
}
template <class T>
T mmin(T a, T b) {
  return a < b ? a : b;
}
template <class T>
T mmax(T a, T b) {
  return a > b ? a : b;
}
template <class T>
T aabs(T a) {
  return a < 0 ? -a : a;
}
template <class T>
long long dcmp(T a, T b) {
  return a > b;
}
template <long long *a>
long long cmp_a(long long first, long long second) {
  return a[first] < a[second];
}
namespace io {
const long long SIZE = (1 << 21) + 1;
char ibuf[SIZE], *iS, *iT, obuf[SIZE], *oS = obuf, *oT = oS + SIZE - 1, c,
                                       qu[55];
long long f, qr;
inline void flush() {
  fwrite(obuf, 1, oS - obuf, stdout);
  oS = obuf;
}
inline void putc(char first) {
  *oS++ = first;
  if (oS == oT) flush();
}
inline bool read(signed &first) {
  for (f = 1, c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                              (iS == iT ? EOF : *iS++))
                            : *iS++);
       c < '0' || c > '9';
       c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    if (c == '-')
      f = -1;
    else if (c == EOF)
      return 0;
  for (first = 0; c <= '9' && c >= '0';
       c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    first = first * 10 + (c & 15);
  first *= f;
  return 1;
}
inline bool read(long long &first) {
  for (f = 1, c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                              (iS == iT ? EOF : *iS++))
                            : *iS++);
       c < '0' || c > '9';
       c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    if (c == '-')
      f = -1;
    else if (c == EOF)
      return 0;
  for (first = 0; c <= '9' && c >= '0';
       c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    first = first * 10 + (c & 15);
  first *= f;
  return 1;
}
inline bool read(char &first) {
  first = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                       (iS == iT ? EOF : *iS++))
                    : *iS++);
  return first != EOF;
}
inline bool read(char *first) {
  while ((*first = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                                (iS == iT ? EOF : *iS++))
                             : *iS++)) == '\n' ||
         *first == ' ' || *first == '\r')
    if (*first == EOF) return 0;
  while (!(*first == '\n' || *first == ' ' || *first == '\r' || *first == EOF))
    *(++first) = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, SIZE, stdin),
                              (iS == iT ? EOF : *iS++))
                           : *iS++);
  *first = 0;
  return 1;
}
template <typename A, typename... B>
inline bool read(A &first, B &...second) {
  return read(first) && read(second...);
}
inline bool write(signed first) {
  if (!first) putc('0');
  if (first < 0) putc('-'), first = -first;
  while (first) qu[++qr] = first % 10 + '0', first /= 10;
  while (qr) putc(qu[qr--]);
  return 0;
}
inline bool write(long long first) {
  if (!first) putc('0');
  if (first < 0) putc('-'), first = -first;
  while (first) qu[++qr] = first % 10 + '0', first /= 10;
  while (qr) putc(qu[qr--]);
  return 0;
}
inline bool write(char first) {
  putc(first);
  return 0;
}
inline bool write(const char *first) {
  while (*first) {
    putc(*first);
    ++first;
  }
  return 0;
}
inline bool write(char *first) {
  while (*first) {
    putc(*first);
    ++first;
  }
  return 0;
}
template <typename A, typename... B>
inline bool write(A first, B... second) {
  return write(first) || write(second...);
}
struct Flusher_ {
  ~Flusher_() { flush(); }
} io_flusher_;
}  // namespace io
using io ::putc;
using io ::read;
using io ::write;
long long inf;
struct _init_ {
  _init_() { memset(&inf, 0x3f, sizeof(inf)); }
};
_init_ ___INIT__;
long long a[20005], b[20005];
long long f[40005], beg[20005];
vector<long long> poly[40005];
long long t;
const long long p = 998244353, g = 3;
long long rev[1 << 18];
long long fpm(long long a, long long b) {
  long long c = 1;
  for (; b; b >>= 1, a = a * a % p)
    if (b & 1) c = c * a % p;
  return c;
}
void NTT(vector<long long> &a, long long n, long long flg) {
  for (long long i = 0; i < n; ++i) {
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) * (n >> 1));
    if (i < rev[i]) swap(a[i], a[rev[i]]);
  }
  for (long long i = 1; i < n; i <<= 1) {
    long long ww = fpm(g, (p - 1) / i / 2 * (flg + p - 1)), w;
    for (long long j = 0; j < n; j += i + i) {
      w = 1;
      for (long long k = 0; k < i; ++k) {
        long long u = a[j + k], v = a[j + k + i] * w % p;
        a[j + k] = (u + v) % p;
        a[j + k + i] = (u - v + p) % p;
        w = w * ww % p;
      }
    }
  }
  if (flg == -1) {
    long long in = fpm(n, p - 2);
    for (long long i = 0; i < n; ++i) a[i] = a[i] * in % p;
  }
}
void Prod(vector<long long> &a, vector<long long> &b, vector<long long> &c) {
  long long first = a.size() + b.size(), n = 1;
  while (n < first) n <<= 1;
  a.resize(n);
  b.resize(n);
  c.resize(n);
  NTT(a, n, 1);
  NTT(b, n, 1);
  for (long long i = 0; i < n; ++i) c[i] = a[i] * b[i] % p;
  NTT(c, n, -1);
  c.resize(first - 1);
  a.clear();
  b.clear();
}
long long query(long long k) {
  long long l = 1;
  while (l < t) {
    Prod(poly[l], poly[l + 1], poly[++t]);
    l += 2;
  }
  return poly[t][k];
}
signed main() {
  long long n, k;
  read(n, k);
  for (long long i = 1; i <= n; ++i) read(a[i]);
  long long q;
  long long tp, first, l, r, d;
  read(q);
  for (; q; --q) {
    read(tp, first, l);
    if (tp == 1) {
      read(d);
      for (long long i = 1; i <= n; ++i) {
        poly[i].clear();
        poly[i].push_back(1);
        poly[i].push_back((first - (i == l ? d : a[i]) + 2 * p) % p);
      }
    } else {
      read(r, d);
      for (long long i = 1; i <= n; ++i) {
        poly[i].clear();
        poly[i].push_back(1);
        poly[i].push_back((first - a[i] + 2 * p) % p);
      }
      for (long long i = l; i <= r; ++i)
        poly[i][1] = (poly[i][1] + 2 * p - d) % p;
    }
    t = n;
    write(query(k), '\n');
  }
  return 0;
}