#include using namespace std; #define REP(i,a,b) for(i=a;i'9')break;*x=(*x)*10+k-'0';}if(m)(*x)=-(*x);} void reader(ll *x){int k,m=0;*x=0;for(;;){mygc(k);if(k=='-'){m=1;break;}if('0'<=k&&k<='9'){*x=k-'0';break;}}for(;;){mygc(k);if(k<'0'||k>'9')break;*x=(*x)*10+k-'0';}if(m)(*x)=-(*x);} void reader(double *x){scanf("%lf",x);} int reader(char c[]){int i,s=0;for(;;){mygc(i);if(i!=' '&&i!='\n'&&i!='\r'&&i!='\t'&&i!=EOF) break;}c[s++]=i;for(;;){mygc(i);if(i==' '||i=='\n'||i=='\r'||i=='\t'||i==EOF) break;c[s++]=i;}c[s]='\0';return s;} template void reader(T *x, S *y){reader(x);reader(y);} template void reader(T *x, S *y, U *z){reader(x);reader(y);reader(z);} template void reader(T *x, S *y, U *z, V *w){reader(x);reader(y);reader(z);reader(w);} void writer(int x, char c){int s=0,m=0;char f[10];if(x<0)m=1,x=-x;while(x)f[s++]=x%10,x/=10;if(!s)f[s++]=0;if(m)mypc('-');while(s--)mypc(f[s]+'0');mypc(c);} void writer(ll x, char c){int s=0,m=0;char f[20];if(x<0)m=1,x=-x;while(x)f[s++]=x%10,x/=10;if(!s)f[s++]=0;if(m)mypc('-');while(s--)mypc(f[s]+'0');mypc(c);} void writer(double x, char c){printf("%.15f",x);mypc(c);} void writer(const char c[]){int i;for(i=0;c[i]!='\0';i++)mypc(c[i]);} void writer(const char x[], char c){int i;for(i=0;x[i]!='\0';i++)mypc(x[i]);mypc(c);} template void writerLn(T x){writer(x,'\n');} template void writerLn(T x, S y){writer(x,' ');writer(y,'\n');} template void writerLn(T x, S y, U z){writer(x,' ');writer(y,' ');writer(z,'\n');} template void writerArr(T x[], int n){int i;if(!n){mypc('\n');return;}rep(i,n-1)writer(x[i],' ');writer(x[n-1],'\n');} char memarr[17000000]; void *mem = memarr; #define MD 1000000007 struct llModMatrix{ int r, c, mod; ll limit; ll **data; void malloc(int r, int c, int mod){int i;this->r=r;this->c=c;this->mod=mod;limit=((1ULL<<63)-1)-(ull)(mod-1)*(mod-1);data=(ll**)std::malloc(sizeof(ll*)*r);data[0]=(ll*)std::malloc(sizeof(ll)*r*c);REP(i,1,r)data[i]=data[i-1]+c;} void* malloc(int r, int c, int mod, void *workMemory){int i;this->r=r;this->c=c;this->mod=mod;limit=((1ULL<<63)-1)-(ull)(mod-1)*(mod-1);data=(ll**)workMemory;data[0]=(ll*)(data+r);REP(i,1,r)data[i]=data[i-1]+c;return (void*)(data[0]+r*c);} void free(void){std::free(data[0]);std::free(data);} void setIdentity(){int i,j;rep(i,r)rep(j,c){data[i][j]=0;if(i==j)data[i][j]=1;}} void setZero(){int i,j;rep(i,r)rep(j,c)data[i][j]=0;} void operator=(llModMatrix &a){int i,j;r=a.r;c=a.c;rep(i,r)rep(j,c)data[i][j]=a.data[i][j];} void operator+=(llModMatrix &a){int i,j;rep(i,r)rep(j,c){data[i][j]+=a.data[i][j];if(data[i][j]>=mod)data[i][j]-=mod;if(data[i][j]<=-mod)data[i][j]+=mod;}} void operator-=(llModMatrix &a){int i,j;rep(i,r)rep(j,c){data[i][j]-=a.data[i][j];if(data[i][j]>=mod)data[i][j]-=mod;if(data[i][j]<=-mod)data[i][j]+=mod;}} void mixed(void){int i,j;rep(i,r)rep(j,c){if(data[i][j]<0)data[i][j]+=mod;if(data[i][j]&&rand()%2)data[i][j]-=mod;}} void add(llModMatrix &a, llModMatrix &b){int i,j;r=a.r;c=a.c;rep(i,r)rep(j,c){data[i][j]=a.data[i][j]+b.data[i][j];if(data[i][j]>=mod)data[i][j]-=mod;if(data[i][j]<=-mod)data[i][j]+=mod;}} void sub(llModMatrix &a, llModMatrix &b){int i,j;r=a.r;c=a.c;rep(i,r)rep(j,c){data[i][j]=a.data[i][j]-b.data[i][j];if(data[i][j]>=mod)data[i][j]-=mod;if(data[i][j]<=-mod)data[i][j]+=mod;}} void mul(llModMatrix &a, llModMatrix &b){int i,j,k;r=a.r;c=b.c;setZero();rep(i,r)rep(k,a.c)if(a.data[i][k])rep(j,c){data[i][j]+=a.data[i][k]*b.data[k][j];if(data[i][j]>=limit||data[i][j]<=-limit)data[i][j]%=mod;}rep(i,r)rep(j,c)if(data[i][j]>=mod||data[i][j]<=-mod)data[i][j]%=mod;} void pow(llModMatrix &a, ull b, void *workMemory){llModMatrix t1,t2;r=c=a.r;workMemory=t1.malloc(r,c,mod,workMemory);workMemory=t2.malloc(r,c,mod,workMemory);setIdentity();t1=a;while(b){if(b%2){t2=*this;this->mul(t2,t1);}t2.mul(t1,t1);t1=t2;b/=2;}} }; struct llModMatrixFastPowVec{ llModMatrix A[64]; int n, mod; ll limit; ll *s, *t; void* set(llModMatrix &m, void *mem, int mx = 64){ int i; n = m.r; mod = m.mod; limit = m.limit; rep(i,mx) mem = A[i].malloc(n,n,m.mod,mem); A[0] = m; REP(i,1,mx) A[i].mul(A[i-1],A[i-1]); s = (ll*)mem; t = s + n; return (void*)(t + n); } ll get(ull a, ll x[], ll res[]=NULL){ int i, j, k, p = 0; ll r = 0; rep(i,n) s[i] = x[i]; for(;a;p++,a/=2) if(a%2){ rep(i,n) t[i] = 0; rep(i,n) rep(j,n){ t[i] += A[p].data[i][j] * s[j]; if(t[i]<-limit||t[i]>limit) t[i] %= mod; } rep(i,n) s[i] = t[i] % mod; } if(res != NULL) rep(i,n) res[i] = s[i]; rep(i,n) r += s[i]; r %= mod; if(r<0) r += mod; return r; } }; ull pw(ull a, ull b, ull m){ull r=1;while(b){if(b&1)r=r*a%m;b>>=1;a=a*a%m;}return r;} int N; ll C[100000], D[100000]; char buf[10000]; int main(){ int i, j, k; ll res = 1, tmp; llModMatrix mt; ll x[2] = {1,0}; llModMatrixFastPowVec sol; mem = mt.malloc(2,2,MD,mem); mt.data[0][0]=0; mt.data[0][1]=1; mt.data[1][0]=1; mt.data[1][1]=1; mem = sol.set(mt,mem); reader(&N); rep(i,N){ reader(C+i); k = reader(buf); D[i] = 0; rep(j,k){ D[i] = D[i] * 10 + buf[j]-'0'; if(D[i] > 100000000000000000LL) D[i] %= MD-1; } D[i] %= MD-1; } rep(i,N){ tmp = sol.get(C[i]+1, x); if(tmp==0){ res=0; continue; } res = (res * pw(tmp, D[i], MD)) % MD; } writerLn(res); return 0; }