int main() {
int n, Q;
scanf("%d%d", &n, &Q);
mod = n + 1;
for ( int i = 0; i < n; i ++ ) {
scanf("%d", &A[i]); A[i] %= mod;
}
for ( int i = 0; i < n; i ++ ) {
scanf("%d", &B[i]); B[i] %= mod;
}
root = getDiscreteRoot(n + 1);
memcpy(coef, A, sizeof(coef));
fft(0, 1, n, 0);
memcpy(resA, res, sizeof(res));
memcpy(coef, B, sizeof(coef));
fft(0, 1, n, 0);
memcpy(resB, res, sizeof(res));
for ( int i = 0; i < n; i ++ )
C[i] = mul(resA[i], powMod(resB[i], Q));
memcpy(coef, C, sizeof(coef));
fft(0, 1, n, 1);
memcpy(resC, res, sizeof(res));
for ( int i = 0; i < n; i ++ ) resC[i] = mul(resC[i], powMod(n, mod - 2));
for ( int i = 0; i < n; i ++ ) printf("%d\n", resC[i]);
}
int superPow(int a, vector<int>& b) {
if(b.empty())
return 1;
int m = b.back();
b.pop_back();
return powMod(superPow(a, b), 10) * powMod(a, m) % base;
}
bool millerRabin(num n, num witness) {
if (n == 2 || n == 3)
return true;
if (n <= 1 || !(n & 1))
return false;
// Write n-1 as m*2^k by factoring powers of 2 from n-1
int k = 0;
for (num i = n - 1; !(i & 1); i >>= 1) {
++k;
}
num m = (n - 1) / (1 << k);
num x = powMod(witness, m, n);
if (x == 1 || x == n - 1)
return true;
for (int r = 1; r <= k - 1; ++r) {
x = powMod(x, 2, n);
if (x == 1)
return false;
if (x == n - 1)
return true;
}
return false;
}
int superPow(int a, vector<int>& b) {
int n = b.size();
if (n == 0) {
return 1;
}
int power = 1;
a = a % MODBASE;
for (int i = 0; i < n; i++) {
power = (powMod(power, 10) * powMod(a, b[i])) % MODBASE;
}
return power;
}
void fft(int delta, int step, int size, bool nega) {
if ( size == 1 ) { res[delta] = coef[delta]; return; }
int k;
for ( k = 2; ; k ++ ) if ( size % k == 0 ) break;
for ( int i = 0; i < k; i ++ ) fft(delta + i * step, step * k, size / k, nega);
int acc = 1, pri = powMod(root, (mod - 1) / size);
if ( nega ) pri = powMod(pri, mod - 2);
for ( int i = 0; i < size; i ++, acc = mul(acc, pri) ) {
tmp[delta + i * step] = 0;
for ( int j = 0, cur = 1; j < k; j ++, cur = mul(cur, acc) )
add(tmp[delta + i * step], mul(cur, res[delta + j * step + (i % (size / k)) * step * k]));
}
for ( int i = 0; i < size; i ++ ) res[delta + i * step] = tmp[delta + i * step];
}
Int geometricProgression(Int x,Int k,Int m){
if(k==0)return 0;
Int s=geometricProgression(x,k/2,m),t=powMod(x,k/2,m);
s=s*(t+1)%m;
if(k%2==1)s=(s*x+1)%=m;
return s;
}
void solve(int a, int b, int p)
{
if (!b) {
outDate(0);
return;
}
int g = PriRoot(p);
int x = BSGS(g, b, p);
LL y, t, d = ext_gcd(a, p-1, y, t);
if (x == -1 || x%d) {
puts("Transmission error");
return;
}
/*
y=(y*(x/d))%(p-1);
d=(p-1)/d;
int ti = 0;
for (y=(y%d+d)%d;y<p-1;y+=d)
rec[ti++] = powMod(g,y,p);
d = ti;
*/
y %= (p-1)/d;
if (y < 0) y += (p-1)/d;
for (int i = 0; i < d; ++i) {
LL ty = y*(x/d)+(p-1)/d*i;
rec[i] = powMod(g, ty, p);
}
std::sort(rec, rec + d);
for (int i = 0; i < d; ++i) outDate(rec[i]);
}
long long gao(long long a, long long b) {
if (b == 1) {
return 0;
} else {
long long d = phi(b);
return powMod(a, d + gao(a, d), b);
}
}
int getDiscreteRoot(int p) {
for ( int x = 2; ; x ++ ) {
bool fail = false;
for ( int y = 2; !fail && y * y <= p; y ++ )
if ( (p - 1) % y == 0 && powMod(x, (p - 1) / y) == 1 )
fail = true;
if ( ! fail ) return x;
}
}
int main() {
freopen("t.in", "r", stdin);
scanf("%d", &d);
scanf("%s", str);
n = strlen(str);
int t;
for ( t = n-1; t >= 0 && str[t] == 'z'; t -- );
if ( t == -1 ) {
printf("Impossible\n");
return 0;
}
str[t]++;
for ( int i = t+1; i < n; i ++ )
str[i] = 'a';
powD = powMod(BASE, d-1);
kInv = powMod(BASE, kMod-2);
dfs(0, 0, 0, 1);
printf("Impossible\n");
}
int PriRoot(int p)
{
if (p==2) return 1;
int phi = p - 1, g, i;
Factor(phi);
for (g = 2; g < p; ++g) {
for (i = 0; i < fCnt; ++i)
if (powMod(g, phi/pf[i], p) == 1) break;
if (i == fCnt) break;
}
return g;
}
int primality(int num) {
int randbase, val, i;
if (num == 1) {
return 0;
}
for (i=1; i<=100 && i<=num; i++) {
randbase = (rand() % (num - 1)) + 1;
val = powMod(randbase, num - 1, num);
if (val != 1) {
return 0;
}
}
return 1;
}
vector<int> QuadraticResidue(LL a, LL b, LL c, int P) {
int h, t; LL r1, r2, delta, pb = 0;
a = normalize(a, P); b = normalize(b, P); c = normalize(c, P);
if (P == 2) { vector<int> res;
if (c % P == 0) res.push_back(0);
if ((a + b + c) % P == 0) res.push_back(1);
return res;
} delta = b * rev(a + a, P) % P;
a = normalize(-c * rev(a, P) + delta * delta, P);
if (powMod(a, P / 2, P) + 1 == P) return vector<int>(0);
for (t = 0, h = P / 2; h % 2 == 0; ++t, h /= 2);
r1 = powMod(a, h / 2, P);
if (t > 0) { do b = random() % (P - 2) + 2;
while (powMod(b, P / 2, P) + 1 != P); }
for (int i = 1; i <= t; ++i) {
LL d = r1 * r1 % P * a % P;
for (int j = 1; j <= t - i; ++j) d = d * d % P;
if (d + 1 == P) r1 = r1 * pb % P; pb = pb * pb % P;
} r1 = a * r1 % P; r2 = P - r1;
r1 = normalize(r1 - delta, P); r2 = normalize(r2 - delta, P);
if (r1 > r2) swap(r1, r2); vector<int> res(1, r1);
if (r1 != r2) res.push_back(r2);
return res;
}
int primality(int num) {
int randbase, val, i;
srand(time(NULL));
if (num == 1) {
return 0;
}
for (i=1; i<=100 && i<=num; i++) {
randbase = (rand() % (num - 1)) + 1;
printf("%d\n", randbase);
val = powMod(randbase, num - 1, num);
if (val != 1) {
return 0;
}
}
return 1;
}
bool BigInt::isPrime() {
BigInt* curr = new BigInt(2);
BigInt* end = new BigInt(200);
BigInt* base = new BigInt();
BigInt* deg = (new BigInt(*this))->sub(*ONE);
bool ret = true;
while (*curr < *end) {
base->copy(*this);
if (*base->mod(*curr) == *ZERO) {
ret = false;
break;
}
curr->add(*ONE);
}
delete curr;
delete end;
delete base;
vector<BigInt*> *data = new vector<BigInt*> ();
for (int i = 0; i < 200; ++i) {
data->push_back(new BigInt(rand()));
}
powMod(data, *deg, *this);
for(int i = 0; i < data->size(); ++i) {
if(ret && *data->at(i) != *ONE) {
ret = false;
}
delete data->at(i);
}
delete data;
delete deg;
return ret;
}
void solve(int a, int b, int p)
{
if (!b) {
outDate(0);
return;
}
int g = PriRoot(p);
int x = BSGS(g, b, p);
LL y, t, d = ext_gcd(a, p-1, y, t);
y %= (p-1)/d;
if (y < 0) y += (p-1)/d;
// printf("%d %d %d %d\n", g, x, y, d);
if (x == -1 || x%d) {
puts("Transmission error");
return;
}
for (int i = 0; i < d; ++i) {
LL ty = y*(x/d)+(p-1)/d*i;
rec[i] = powMod(g, ty, p);
}
std::sort(rec, rec + d);
for (int i = 0; i < d; ++i) outDate(rec[i]);
}
int main() {
freopen("t.in", "r", stdin);
prework();
// check();
int TST;
scanf("%d", &TST);
while ( TST -- ) {
scanf("%d", &K);
for ( int i = 0; i < K; i ++ ) {
scanf("%d%d", &A[i], &B[i]);
}
int ans = 0;
for ( int d = 1; d <= B[0]; d ++ ) {
int acc = phi[d];
for ( int i = 0; i < K; i ++ )
acc = mul(acc, B[i]/d-(A[i]-1)/d);
add(ans, acc);
}
for ( int i = 0; i < K; i ++ )
ans = mul(ans, powMod(B[i]-A[i]+1, kMod-2));
ans = (-ans + kMod) % kMod;
printf("%d\n", ans);
}
}
Int powMod(const Int &x, const Int &k, const Int &m) {
if (k == 0) return 1;
if (k % 2 == 0) return powMod(x*x % m, k/2, m);
else return x*powMod(x, k-1, m) % m;
}
Hash operator + (const Hash&b) {
return Hash(len + b.len, value * powMod(MAGIC, b.len) + b.value);
}
int main(int argc, char* argv[])
{
char *file1 = argv[1];
char *file2 = argv[3];
char *file3 = argv[4];
char *file4 = NULL;
char op = argv[2][0];
int bin = 0;
struct bNum n, m, md;
if (argc == 6)
{
if (!strcmp(argv[5], "-b"))
bin = 1;
else
file4 = argv[5];
}
if (argc == 7)
{
bin = 1;
file4 = argv[6];
}
if (bin == 1)
{
n = ReadFromBFile(file1);
m = ReadFromBFile(file2);
if (file4 != NULL)
md = ReadFromBFile(file4);
}
else
{
n = ReadFromTFile(file1);
m = ReadFromTFile(file2);
if (file4 != NULL)
md = ReadFromTFile(file4);
}
struct bNum k;
k.size = 0;
k.sign = 0;
k.nums = NULL;
if (argv[2][0] == '+')
k = Sum1(n, m);
if (argv[2][0] == '-')
{
struct bNum minusB = mins(m);
k = Sum1(n, minusB);
free(minusB.nums);
}
if (argv[2][0] == '*')
k = mul(n, m);
if (argv[2][0] == '/')
{
struct bNum q;
k = dividing(n, m, &q);
free(q.nums);
}
if (argv[2][0] == '%')
{
struct bNum q = dividing(n, m, &k);
free(q.nums);
}
if (file4 != NULL)
{
struct bNum tmp;
struct bNum q = dividing(k, md, &tmp);
free(q.nums);
free(k.nums);
k = tmp;
}
if (argv[2][0] == '^')
{
if (file4 == NULL)
k = pPow(n, m);
else
k = powMod(n, m, md);
}
if (bin == 1)
WriteToBFile(file3, k);
else
WriteToTFile(file3, k);
free(n.nums);
free(m.nums);
free(k.nums);
if (file4 != NULL)
free(md.nums);
return 0;
}
